
Class jBJ 
Book_ 



_^„ 



PRESENTED BY 



^-7— ■■■■■■ HH 



MENTAL FATIGUE 

DURING CONTINUOUS EXERCISE OF 
A SINGLE FUNCTION 



BY 

THOMAS RUSSELL GARTH 



Submitted in partial fulfillment of the requirements 

for the degree of Doctor of Philosophy in the 

Faculty of Philosophy, Columbia University 



1918 




7 



/ 






MENTAL FATIGUE 



Digitized by the Internet Archive 
in 2011 with funding from 
The Library of Congress 



http://www.archive.org/details/mentalfatiguedurOOgart 



MENTAL FATIGUE 

DURING CONTINUOUS EXERCISE OF 
A SINGLE FUNCTION 



BY 

THOMAS RUSSELL GARTH 



Submitted in partial fulfillment of the requirements 

for the degree of Doctor of Philosophy in the 

Faculty of Philosophy, Columbia University 



'^^ ^\ /V^V^^*"^ »K-*fA 



1918 



.G;3 



m 21 isis 



The writer makes the following acknowledgments: To Dr. R. S. 
Woodworth for valuable suggestions in the handling of the data 
and criticism of the calculations; to Dr. E. L. Thorndike for use 
of his addition sheets and suggestions as to the conduct of the ex- 
periment; to his wife, Ethel Nadine Garth, who corrected some of 
the sheets and assisted in the tabulation and without whose en- 
couragement the enormous task of correcting the 12,355 papers 
and that of their tabulation and the many and various calculations 
might never have been brought to completion. My thanks are due 
also to Dr. J. A. C. Chandler, Superintendent of City Schools of 
Richmond, Va., and his first assistant, Mr. A. H. Hill, for access 
to the classes of the schools of that city; to Mr. F. M. Martin for 
the same courtesy in the Petersburg, Va., schools, and to the prin- 
cipals and teachers who rendered valuable assistance in giving the 
tests; and to Mr. S. P. Duke, Head of the Department of Educa- 
tion of the State Normal School of Farmville, Va., for much appre- 
ciated assistance while tests were being given in Richmond. 



INTRODUCTION 

A SURVEY OF THE SUBJECT OF MENTAL FATIGUE 
DURING CONTINUOUS EXERCISE OF A SINGLE FUNCTION 

So far the investigations of various experimenters in the field of 
Mental Fatigue during continuous exercise show that continuous 
work under the lash of keen motivation reduces the efficiency only 
slightly, even though the subjects worked from one to two hours. 
Burgerstein, 'pi, found in an experiment with a large group of boys, 
aged eleven to thirteen years, in which the pupils performed easy 
examples in addition and multiplication in ten-minute periods with 
five-minute rests between, that the number of examples increased 
as the test proceeded, but there were more errors and corrections 
made by the pupils as the work went on. 

Hopner, '94, undertaking to make the exercise more like that of 
the ordinary recitation, had a class of forty-six boys, of average age, 
nine years, write nineteen sentences from dictation. Each sentence 
was read aloud to the class once, then it was repeated once by a 
single pupil, next by the entire class, and then the pupils were re- 
quired to write it from memory. The experiment extended over 
two hours. Hopner found that as the time proceeded, the pupils 
became less exact. Colloquial speech often took the place of the 
words in the dictated sentence. It is very evident that the materials 
for the experiment were not of equal difficulty. Neither were the 
pupils pressed to their utmost. (Offner & Whipple, Mental Fatigue, 

57ff.) 

Holmes, '95, had children from Grades Three to Eight add num- 
bers for thirty-six minutes and broke the time into four periods of 
nine minutes each. There was an increase in errors of adding and 
copying. But when everything in the way of length of problem 
and speed is taken into consideration, the decrease in efficiency is 
not very great. 

Cattell and Dolley found that simple reaction-time is not influ- 
enced by previous reactions to any great extent. 



Vlll INTRODUCTION 

Thorndike describes an experiment of continuous mental work 
"of from three to eight hours" which "failed in the case of Dr. R. S. 
Woodworth, to produce any demonstrable diminution in efficiency." 
One part of the experiment was to mark the e's and t's in a book of 
151 pages. This process continued for eight hours with less than 
nine minutes interruption. (See Thorndike's Educational Psy- 
chology, Vol. Ill, pp. 29-32.) Thorndike, 'u, had fourteen students 
work from four to fourteen hours doing mental multiplication of 
three-place numbers by a like number. Six of these individuals 
took fifty-four per cent, more time for the end of the period on one 
day than they did at the beginning of the period for the preceding 
day. Six others had an average increase of fifty-nine per cent. 
For the other two, the increase was twenty-one per cent. 

Arai, '12, had eleven students perform multiplication of two-place 
numbers mentally for two hours on two occasions. The intermis- 
sions were not the same for all participants in the experiment. The 
measure of efficiency was the time required for each example. It 
was found that the time was reduced. In performing the multi- 
plications this means that there was an increase in efficiency. 

Kraepelin worked out a method for continuous adding. A note- 
book is prepared with numbers printed in vertical columns. A 
bell is made to ring every five minutes and when the subject hears 
the bell he makes a mark. In this way the record is made according 
to the time worked. Kraepelin and his followers (Offner & Whipple, 
pp. 62-73) claim to have found certain interesting features in the 
work curve. These are practice, warming-up (Anlauf), swing 
(Anregung), spurt (Antrieb), initial spurt if it occurs at the 
beginning and 'spurt of change' if it occurs when a new kind of 
work begins, and 'terminal' spurt or end spurt (Schlussantrieb) 
when the subject realizes that he is nearing the end of the experi- 
ment or exercise. 

Thorndike's absolutely fair treatment of the results and data of 
Kraepelin's work and of those who follow him brings into question 
the existence of such features in all work curves, and calls for further 
proof of their existence. He says: "Two hours or less of continu- 
ous exercise of a function at maximum efficiency produce a tempo- 
rary negative effect . ... of not over ten per cent, and in most func- 
tions still less than that." * 

1 Educational Psychology, Vol. Ill, pp. 68-69. 



— m 



INTRODUCTION IX 

F. M. Phillips, Journal of Educational Psychology, 191 6, had 
pupils of school grades of Fourth to Eighth work for ten minutes 
on arithmetic problems of addition, subtraction, multiplication and 
division. At the end of each minute the subject made a mark on 
the paper so that the experimenter knew what was done each 
minute by the subjects. In all the processes the best work was 
accomplished during the first minute. But the experimenter did 
not undertake to show whether there was fatigue or not. He 
found correlations between the first and last periods, in all the 
processes, ranging from .54 to .73, and says that the work of the 
first minute is less variable than that of later minutes, and that it 
is a fair index in all probability of one's ability in arithmetic. 

W. S. Painter, Journal of Educational Psychology, 1916, did mental 
multiplication of four-place numbers after much mental and physi- 
cal work which had resulted in a feeling of fatigue. He worked 
from 11 p. m. until 3:07 a. m. During the latter part of the experi- 
ment there was "a marked rise in time" per problem and the experi- 
menter thinks that "the outcome suggests strongly that there 
exists a definite and relatively abruptly appearing point beyond 
which mental work becomes impossible." While the time in per- 
forming the last three multiplications is high, the errors are rela- 
tively few. Mr. Painter believes, however, that after this abrupt 
point all mental work, properly so called, was practically impossible. 



__ 



CHAPTER I 
THE ADMINISTRATION OF THE EXPERIMENT 

The Subjects of the Experiment 

There were seven hundred and eleven subjects in these experi- 
ments. Three hundred and sixty-eight of them were children in 
the Third and Fourth grades, and three hundred and forty-three 
of them were children of the Seventh and Eighth grades of the 
public schools of Virginia, all white children. A large part of the 
number was from the city schools of Richmond and Petersburg. 
The smaller part was from the Training School of the State Normal 
School at Farmville, Va., and the public schools of Farmville, Va. 
The boys and girls were about equally divided and their ages were 
those of the average for the grades in which the tests were given. 
There was absolutely no selecting of subjects, but the experimenter 
took the cases where he could get them. For this reason it may be 
taken as a fact that the results represent the work of the average 
child of these grades. 

Materials Used 

The materials used were the Thorndike addition sheets, such as 
those used by Kirby in the experiment described in his "Practice 
in the Case of School Children," Teachers College, Columbia Uni- 
versity Contributions to Education, No. 53. There are seven differ- 
ent sheets. Each has forty-eight columns of one-place numbers, 
each column contains ten addends with the i's and the o's omitted, 
and each column is so arranged that any successive five of the 
columns are of a difficulty nearly, if not exactly, equal. These 
sheets were arranged in pads. For the Third and Fourth grades 
there were fourteen sheets, and for the Seventh and Eighth grade 
group there were twenty-one sheets in a pad. There was no possi- 
bility of a child's remembering the answers on a sheet which re- 
curred, because there would be no way of identifying that sheet. 
Eye strain was reduced to a minimum because the type is so very 
large, and besides, the eyes got a rest every two minutes. 



2 MENTAL FATIGUE DURING CONTINUOUS EXERCISE 

Conditions of the Experiment 

Since the purpose of the experiment was to ascertain the be- 
havior of the child mind during a recitation, both the materials 
and the conditions of the experiment were made as nearly like a 
recitation — or a drill recitation — as was possible under the circum- 
stances. The materials were ordinary addition problems of one 
column, such as a teacher might use for a drill on adding and for 
improvement in number combinations. The experimenter gave 
all the tests in the presence of the regular teacher, and relied on his 
own teaching experience to put the child perfectly at his ease. 
There was nothing strained or strange about the experimenter's 
attitude but there was a constant endeavor to make the manner 
and atmosphere of the experiment entirely like that of an ordinary 
recitation-drill. 

The subjects were told that the experimenter wished to find out 
who was the best adder in the class and that papers would be 
passed for this purpose, if the class was agreeable to it. The stu- 
dents were usually eager to try. They were told that the papers 
would be examined and that the name of the best adder would be 
announced later on by the teacher. The pads were then passed to 
the pupils, face downward. The experimenter used a stop watch. 
At a signal the pupils turned the pads face upward and added for 
two minutes when time was called. As quickly as possible with no 
intentional intermission except such as was necessary to keep the 
class together, the class received the instruction to "take the next 
sheet" and the signal "go" was given, when they again worked two 
minutes by the stop watch. The intermissions were only about 
ten seconds long. But in this time the subjects raised their eyes 
to the experimenter who tried to maintain a 'sympathetic' counte- 
nance such as would keep them working happily. Nothing more 
was said to the class by the experimenter after the initial motiva- 
tion, excepting "take the next paper — get ready — go!" and after 
they had worked two minutes, "stop." The Third and Fourth grade 
pupils worked thus for twenty-eight minutes, and the Seventh and 
Eighth grade pupils for forty-two minutes. 

The pads supplied a record of what was done every two minutes 
by each pupil. After the total time had passed the pads were col- 
lected. Each pad bore the name, age, and school and grade of the 
pupil on the back written by the pupil when he received the pad. 



ADMINISTRATION OF THE EXPERIMENT 3 

Method of Scoring 

With fourteen sheets to every one of the 368 Third and Fourth 
grade pupils and 21 sheets to every 343 Seventh and Eighth grade 
pupils, the experimenter secured 12,355 papers. For the Third and 
Fourth grades there were fourteen periods of two minutes each and 
for the older group there were twenty-one periods of two minutes 
each. When these papers were examined, a record was made of 
what each child attempted each two minutes, and another record 
of the accuracy of each child for every two-minute period. If a 
child attempted six columns, he received a credit for that two min- 
utes of six columns attempted. If only four of these were correct, 
he received credit on the accurate record sheet of only four columns. 
These two records, one of attempts and one of accurates, gave two 
tables, in the one case having fourteen columns 368 figures long, and 
in the other having twenty-one columns 343 figures long for at- 
tempts, and likewise the same for accurates. In short, we should 
say that the two groups of children — Third and Fourth grades and 
Seventh and Eighth grades — had two arrays of results, one for 
attempts and one for accurates. 

If a child's record showed itself incomplete — nothing attempted 
after a certain time — except in the last period or so, his work was 
not counted in the experiment. One child had to stop because of a 
slight illness which she had when she came to school that morning. 
Another boy was convalescent from typhoid fever and had to stop 
in the midst of the experiment. If a lack-a-daisical attitude toward 
the experiment was evidenced by any great omission of effort 
in the written record, the material was thrown out. But it so hap- 
pened that there was very little that had to be discarded. A child 
was given credit for what he did, both in quantity and quality. 

Time of Day and Year 

According to Heck's 1 experiments, the time of day makes little 
difference and so the experimenter made his tests at any time dur- 
ing the school day — early morning period, noon, and afternoon 
indiscriminately. Since there was a generous sampling of all times 
of the day, no one time of the day with its fatigue could assert itself 

1 W. H. Heck, A Study of Mental Fatigue, 1913. 



4 MENTAL FATIGUE DURING CONTINUOUS EXERCISE 

to any great extent. The test was intended to show what happens 
during a recitation at any time of the day. 

The time of the year was in the fall, in the winter, and in the 
spring. One class took its test when the snow was falling on the 
ground, a large part of the groups took their tests in November, 
and some of the classes worked with the windows open to the spring 
breeze. The tests were given during the time elapsing between 
December, 191 3, and November, 19 14. 






CHAPTER II 
ATTEMPTED AND ACCURATE PERFORMANCE 

The Group Curves 

Four curves are given herewith, plotted from the tables which 
accompany them. There are two work or attempts curves, one for 
Third and Fourth grades and one for Seventh and Eighth grades; 
and there are two accurates curves, respectively, for Third and 
Fourth grades and for Seventh and Eighth grades. In the Third 
and Fourth grade group there were 368 children participating and 



Periods 



FJcc" rehires .. 




a. 



-U U 



4 5 6 7 8 9 10 11 
Fig. I. Third and Fourth Grades 



13 14 



— 



6 MENTAL FATIGUE DURING CONTINUOUS EXERCISE 

in the Seventh and Eighth grade group there were 343 who took 
part. The Third and Fourth grade group worked for twenty-eight 
minutes actually. This time was divided into fourteen periods of 
two minutes each. The horizontal line represents the time, in 
periods, during which the groups worked. The vertical line indi- 
cates the number of columns either attempted or accurately done. 
In the case of the work curve this vertical line indicates columns 
attempted whether right or wrong; in the case of the accuracy curve 

7f 



U 



£> 3 



2 






X.-'^/ 



FJlUitpfs 



ffccurd-Jes 



j Li 



Periods 1 23 4 56 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 
Fig. 2. Seventh and Eighth Grades 

the vertical scale stands for columns correctly added. Every point 
on the curve was ascertained by finding the average attained by 
the group for that identical two-minute period of work. We shall 
call these the group curves. 

These curves are given here for the sake of presenting the facts 
derived by the experiment. These are mere gross results. The 
attempts and accuracy curves derived herewith do not afford a 
true idea of measurement of fatigue of the individuals during the 
work period of twenty-eight minutes for the Third and Fourth 
grade group nor for the forty-two minutes during which the Seventh 
and Eighth grade group worked. If instead of giving the average 



ATTEMPTED AND ACCURATE PERFORMANCE 7 

we gave the quantity obtained by the group, this would emphasize 
the production by the group as a whole. These first curves give 
the changes in the group without regard to the changes of the 
individual. The curves following these will give the average of 
the individual curves and thus will regard individual changes. 

TABLE I 

Attempts of Third and Fourth Grades — Absolute Measures 
Columns attempted for each period of two minutes 



eriod 


Average 


A 


.D. 


P.E 


I 


3. 15 


1 .20 


.058 


2 


3 


35 


1 


17 


.051 


3 


3 


47 


1 


22 


•053 


4 


3 


48 


1 


34 


• 059 


5 


3 


27 


1 


17 


.051 


6 


3 


37 


1 


25 


•055 


7 


3 


45 


1 


34 


• 059 


8 


3 


54 


1 


33 


.058 


9 


3 


55 


1 


38 


.061 


10 


3 


57 


1 


39 


.061 


11 


3 


49 


1 


3i 


•057 


12 


3 


28 


1 


3i 


■057 


13 


3 


5i 


1 


4i 


.062 


H 


3 


38 


I 


36 


.060 



TABLE II 

Accurates of Third and Fourth Grades — Absolute Measures 
Columns accurate for each period of two minutes 



sriod 


Average 


A.D. 


P.E. 


1 


1 .70 


1.27 


.056 


2 


i-93 


1 .1 


.048 


3 


2. 11 


1.32 


.058 


4 


2.06 


1.28 


.056 


5 


1.88 


1. 16 


.051 


6 


2.07 


1.24 


•054 


7 


1.86 


1 .21 


• 053 


8 


1.99 


1. 16 


.051 


9 


1.98 


1-34 


■059 


10 


1 .96 


1.30 


■057 


11 


1.94 


1 .27 


.056 


12 


1.79 


1.30 


•057 


13 


1.82 


1 .21 


•053 


14 


1.78 


1.30 


•057 



MENTAL FATIGUE DURING CONTINUOUS EXERCISE 



TABLE III 

Attempts of Seventh and Eighth Grades — Absolute Measures 
Columns attempted for each period of two minutes 



Period 


Average A 


D. 


P.E. 


I 


6.02 I 


67 


■075 


2 


5.62 I 


39 


.062 


3 


5-77 1 


5 


.068 


4 


5-92 1 


61 


.072 


5 


5 46 1 


5i 


.068 


6 


5.78 1 


55 


.07 


7 


5-64 1 


53 


.069 


8 


5-8i 1 


69 


.076 


9 


5-68 1 


77 


.079 


IO 


5-98 1 


52 


.068 


ii 


5-94 1 


56 


.07 


12 


5.65 1 


69 


.076 


13 


5-99 1 


5 


.068 


14 


5-83 1 


68 


.076 


15 


6.23 1 


95 


.088 


16 


5-91 1 


52 


.068 


17 


6. 11 1 


67 


•075 


18 


5-95 1 


84 


.083 


19 


561 1 


7 


.077 


20 


6.02 1 


78 


.08 


21 


5-99 1 


9i 


.086 



TABLE IV 

Accurates of Seventh and Eighth Grades — Absolute Measures 
Columns accurate for each period of two minutes 



Period 


Average 


^.P. 


P.E. 


1 


4.22 


1.85 


.083 


2 


4 


04 


1.63 


.074 


3 


4 


19 


1.50 


.068 


4 


4 


30 


1.83 


.082 


5 


4 


01 


i-57 


.061 


6 


4 


18 


1.94 


.087 


7 


4 


03 


i-59 


.072 


8 


4 


22 


1 .64 


.074 


9 


4 


64 


1.65 


.073 



ATTEMPTED AND ACCURATE PERFORMANCE 



TABLE IV (Continued) 
Accurates of Seventh and Eighth Grades — Absolute Measures 
Columns accurate for each period of two minutes 



eriod 


Average 


A. D. 


P. E. 


10 


4-31 


1.68 


•075 


ii 


4.29 


1. 71 


.076 


12 


3-89 


1.76 


.079 


13 


4.19 


i-74 


.078 


14 


3-88 


1 .76 


.079 


15 


4.24 


1. 91 


.085 


16 


403 


1. 71 


.077 


17 


4.26 


1 .72 


.077 


18 


4.02 


1 .72 


.077 


19 


3-88 


1.77 


.080 


20 


3-93 


1.83 


.082 


21 


3-74 


1.82 


.081 



Average of the Individual Curves 

The object in a study of this kind is to give every individual, 
whether his work is slow or fast, the same influence upon the final 
average. It is not fair to the poor or weak individual to put his 
small effort on a basis of absolute terms along with the effort of the 
better workers similarly expressed. The former may fatigue while 
the latter gain and a mean between them show essentially the curve 
of the better worker. The original data of the preceding tables fail 
to represent truly the facts which we wish to bring out because, as 
intimated above, the rapid workers with their larger measures of 
performance entirely swamp the changes that may occur in the 
work of the slower ones. But if everyone's work for the successive 
periods' is reduced to percentages of his total, the slow count the 
same as do the fast workers in determining the general work curve. 
For this reason we have derived percentage curves which represent 
more truly than the foregoing curves the central tendency of the 
whole group with regard to fatigue. With the absolute numbers 
we can examine the question of fatigue from the standpoint of one 
interested in the total product of a group, whereas by the personal 
curves we disregard the total products and examine changes in the 



10 



MENTAL FATIGUE DURING CONTINUOUS EXERCISE 



working ability of the individuals, and the general tendency of 
these individual changes. 



r 

-7 
3 






1 - 



T~h 1 yi 3| ?t4 h wftk Cfa 4^-s. 




$ccuv3{te.s 



J L 



i_J 



a / > 



J ¥■ s £ 7 ^ / /* // f>n t* ft y( u^ 






The curves shown herewith (Figures 3 and 4) are, however, only 
slightly different in form from the preceding curves. Every number 
in the distribution is a percentage of the total accomplished during 
the entire period of work for each installment of time for each child. 
A child did so much every two minutes for twenty-eight and forty- 
two minutes in the Third and Fourth grade group and the Seventh 
and Eighth grade group respectively. Percentages of these dis- 



ATTEMPTED AND ACCURATE PERFORMANCE 



II 



tributions were determined by dividing each two minutes' work by 
the total amount added during the whole period of work by each 
individual. This gave fourteen per cents, in the younger group for 
each child, and twenty-one per cents, in the Seventh and Eighth 
grade group for each child of that group. The fourteen average 
per cents, for the Third and Fourth grade group were obtained, 

—>e<fe>fiA -zsriAciphtii trades. 



< 3 



X 
v 

IV, 




Zf& 






o / x j *■ *r <£ 7 8 f >u (' /> '3 **■ T /<° '7 >* '/ -3-v «-/ 



3j)<f,y;4<A*/ Cvrves. 



and the twenty-one average per cents, for the Seventh and Eighth 
grade group likewise were obtained, and these averages give the 
accompanying curves. Every position on the curves indicates the 
central tendency of the relative value in attempts and accuracy of 
the groups for any two minutes of the time of working; and this 
should be taken as meaning the comparative working ability at that 
period. The attempts curve does not signify a pure mental per- 
formance, while the accurates curve here expressed in percentages 
does represent a more nearly pure mental process. 



12 



MENTAL FATIGUE DURING CONTINUOUS EXERCISE 



TABLE V 

Data for the Curves Representing the Average of the Individual 
Curves — Third and Fourth Grades 
Columns attempted in each period of two minutes, expressed 
as a per cent, of the total number attempted 

P.E. 



.09 

.08 
.06 
.06 
.06 
.06 
.06 
.06 
.06 
.06 
.06 
.07 
■05 
.07 



zriod 


Range 


Average 


A 


D 




Per Cent. 


Per Cent. 




1 


0-50 


6.97 


1.94 


2 


0-25 


7.24 


1 


52 


3 


0-17 


7-30 


1 


37 


4 


0-17 


7.24 


1 


40 


5 


0-25 


6.97 


1 


32 


6 


0-14 


7.20 


1 


32 


7 


0-18 


6.97 


1 


35 


8 


0-25 


7.29 


1 


43 


9 


0-17 


7-34 


1 


39 


10 


0-12 


7.28 


1 


44 


11 


0-14 


7.27 


1 


34 


12 


0-13 


6.78 


1 


47 


13 


0-13 


7-25 


1 


31 


14 


0-16 


6.90 
100.00 


1 


62 



TABLE VI 

Data for the Curves Representing the Average of the Individual 

Curves — Third and Fourth Grades 

Columns accurate for each period of two minutes, 

in per cent, of total columns accurate 

P.E. 



20 
22 

21 
13 

19 
18 
18 
18 
21 
19 
19 
18 
19 
17 



mod 


Range 


Average 


A. 


D. 




Per Cent. 


Per Cent. 




1 


O-IOO 


6.13 


4-53 


2 


O-IOO 


8-34 


4 


87 


3 


0-50 


8.16 


4 


34 


4 


o-34 


7-53 


4 


03 


5 


O-IOO 


7.27 


4 


20 


6 


0-50 


7.76 


4 


10 


7 


O-IOO 


6.94 


4 


01 


8 


0-28 


7.24 


4 


05 


9 


O-IOO 


7.62 


4 


57 


10 


0-50 


7.16 


4 


31 


11 


0-29 


7.06 


4 


27 


12 


0-30 


6.10 


4 


07 


13 


0-34 


6.89 


4 


30 


14 


0-40 


5-8o 
100.00 


3 


75 



ATTEMPTED AND ACCURATE PERFORMANCE 

TABLE VII 

Data for the Curve Representing the Average of the Individual 

Curves — Seventh and Eighth Grades 

Columns attempted for each period of two minutes, 

in per cent, of total columns attempted 



13 



eriod 


Range 


Average A 


D. 


P.E 




Per Cent. 


Per Cent. 






1 


2-10 


5.00 1 


01 


•05 


2 


0-10 


4 


86 


79 


.04 


3 


0-9 


4 


67 


77 


.04 


4 


2-10 


4 


79 


69 


•03 


5 


2-8 


4 


37 


75 


•03 


6 


3-8 


4 


73 


72 


•03 


7 


2-8 


5 


30 1 


04 


•05 


8 


i-ii 


4 


63 


79 


.04 


9 


2-9 


4 


59 


75 


•03 


10 


3-8 


4 


86 


75 


•03 


11 


1-8 


4 


80 


68 


•03 


12 


2-10 


4 


43 


74 


.03 


13 


1-16 


4 


42 


88 


.04 


H 


2-7 


4 


68 


83 


.04 


15 


i-9 


5 


58 1 


11 


•05 


16 


1-9 


4 


74 


62 


•03 


17 


0-9 


4 


80 


7i 


•03 


18 


0-9 


4 


75 


90 


.04 


19 


0-8 


4 


40 


86 


.04 


20 


0-9 


4 


84 


9i 


.04 


21 


0-11 


4 


76 


90 


.04 




100 


00 





TABLE VIII 

Data for the Curve Representing the Average of the Individual 

Curves — Seventh and Eighth Grades 

Columns accurate for each period of two minutes, 

in per cent, of total columns accurate 



nod 


Range 


Average 


A 


D. 


P.E 




Per Cent. 


Per Cent. 






1 


0-20 


5.00 


1.74 


.08 


2 


0-14 


4 


85 


1 


5i 


.07 


3 


0-30 


4 


85 


1 


51 


.07 


4 


0-27 


5 


01 


1 


37 


.06 


5 


0-11 


4 


50 


1 


37 


.06 


6 


0-15 


5 


03 


1 


33 


.06 


7 


0-20 


4 


70 


1 


46 


.07 


8 


0-12 


4 


83 


1 


37 


.06 



H 



MENTAL FATIGUE DURING CONTINUOUS EXERCISE 





TABLE VIII (Com 


inuea 


) 


°eriod 


Range 


Average 


A. D 




Per Cent. 


Per Cent. 




9 


0-12 


4-73 


1.30 


IO 


0-22 


5 


15 


1 


48 


ii 


0-17 


5 


10 


1 


28 


12 


0-12 


4 


34 


1 


45 


13 


0-12 


5 


03 


1 


39 


H 


0-10 


4 


37 


1 


5i 


15 


0-13 


4 


90 


1 


4* 


16 


0-13 


4 


74 


1 


55 


17 


0-11 


4 


84 


1 


42 


18 


0-23 


4 


73 


1 


23 


19 


0-13 


4 


40 


1 


35 


20 


0-10 


4 


50 


1 


53 


21 


0-12 


4 


30 


1 


69 




100 


00 





P.E. 

.06 
.07 
.06 
.07 
.06 
.07 
.07 
.07 
.06 
.06 
.06 
.07 
.08 



The Similarity between Attempts and Accurate Performance 

The question arises as to whether the general tendencies of the 
attempts curve and the accurates curve are the same or different. 
Possibly the best evidence that they are rather similar is to be 
gotten by merely examining the curves themselves. (See Figures 
1 to 4.) While the accuracy and attempts curves are not parallel 
they are decidedly similar in their general tendencies. To give 
further evidence of this similarity, correlations, though not as good 
evidence as the curves themselves, were gotten between the two 
kinds of curves. 

The correlations between the Averages of Tables I and II, taken 
as a whole, is +.487. The correlation for the Averages of Tables III 
and IV, taken as a whole, is +.29. For Tables V and VI, and for 
VII and VIII, the correlations are respectively +.58 and +.32. 
The older group has the lower correlations. The curves derived 
from the per cents. — the curves called the average of the individual 
curves — give higher correlations than the curves derived from 
absolute measures. 

Therefore, numbers for attempts and numbers for accurates show 
a positive tendency to vary together. They do not vary inversely, 
if we take the curves as a whole, though doubtless there are corre- 
sponding parts of the curves that do. Some of these divergencies 
will appear as we proceed in our examination of the curves. 



ATTEMPTED AND ACCURATE PERFORMANCE 



15 



I. Maximum period 
II. Minimum period 

III. Average first three periods 

IV. Average last three periods 
V. Per cent, loss or gain 

III and IV 
VI. Average part one (or 
first third of curve) 
VII. Average part two (or 

second third of curve) 
VIII. Average part three (or 
third third of curve) 
IX. VI as base 
VII : VI 
VIII : VI 



TABLE IX 

Absolute Measures 



Third and Fourth 

Grades 

Attempts Accuracy 

Tenth Third 

First First 

3.32 cols. 1. 91 cols. 

3.39 cols. 1.79 cols. 

2.0 gain 6.2 loss 



Seventh and Eighth 

Grades 
Attempts Accuracy 

Fifteenth Ninth 

Fifth Second 

5.80 cols. 4.15 cols. 

5.87 cols. 3.85 cols. 

1.0 gain 7.0 loss 



3.36 cols. 1.95 cols. 5.74 cols. 4.14 cols. 

3.44 cols. 1.96 cols. 5.84 cols. 4.20 cols. 

3.45 cols. 1.86 cols. 5.97 cols. 4.01 cols. 



1. 00 


1. 00 


1. 00 


1. 00 


1.023 


1.005 


1. 017 


1.014 


1.026 


•95 


1.04 


•97 



TABLE X 

From the Data of the Curves Representing the Average 
of the Individual Curves 







Third and Fourth 


Seventh and Eighth 






Grades 


Grades 






Attempts 


Accuracy 


Attempts 


Accuracy 


I. 


Maximum period 


Ninth 


Second 


Fifteenth 


Tenth 


II. 


Minimum period 


Twelfth 


Four- 
teenth 


Fifth 


Twenty- 
first 


III. 


Average first three periods 


7-17% 


7-54% 


4-85% 


4.90% 


IV. 


Average last three periods 


6.98% 


6.26% 


4-67% 


4.40% 


V. 


Per cent, loss or gain 


3.0 loss 


17.0 loss 


4.0 loss 


10.2 loss 


VI. 


Average part one (or 
first third of curve) 


7-19% 


7-54% 


4-82% 


4-85% 


VII. 


Average part two (or 
second third of curve) 


7-15% 


7-37% 


4-63% 


4-79% 


VIII. 


Average part three (or 
third third of curve) 


7-io% 


6.60% 


4.84% 


4-63% 


IX. 


VI as base 


1. 00 


1. 00 


1. 00 


1. 00 




VII : VI 


•99 


.98 


.96 


•99 




VIII : VI 


.98 


.88 


1.004 


•95 



l6 MENTAL FATIGUE DURING CONTINUOUS EXERCISE 

The accompanying tables, Nos. IX and X, give some of the data 
to be derived from the curves. Table IX is a summary of data 
gotten from the absolute measures and Table X is a similar sum- 
mary gotten from the percentages. Using these data of the tables 
we shall discuss various factors which may influence the curves, 
as fatigue, warming-up, initial-spurt, practice, and end-spurt. Ac- 
cordingly, the discussion will be from the two standpoints spoken 
of above, that of one interested in the total product and that of 
one interested in changes in working ability. 

Maximum and Minimum Points on the Curve 

The maximum point on a curve of continuous performance at 
least makes a good landmark for a preliminary survey of fatigue 
in that curve. Being the high point in the curve, the line must 
recede from it, be it ever so gradually, and this negative effect must 
be due to fatigue — granting that the workers are serious in their 
performance. The minimum must mean, if we still grant the 
seriousness of the workers, one of several things, i.e., if it occurs 
before the maximum it must signify a lack of proper adaptation or 
a warming-up, if it follows the maximum it must be due to fatigue 
(from which there may be recovery). The maximum point in the 
curve does not tell us when fatigue begins to work in the perfor- 
mance; but it makes the presence of fatigue evident by the falling 
away that follows it. Consequently, it makes a good point at which 
to begin the discussion of fatigue. 

If the decline in the curve following the maximum was not due 
to fatigue, it must have been due to ennui or loss of interest. It 
might better be said, shifting of interest. Now, because of the 
original strong motivation through appeal to the competitive im- 
pulse and because no other interest was permitted to arise in as 
far as lay within the power of the experimenter to prevent it — for 
the subjects really had no time for mind wandering, and were kept 
steadily at their tasks — for this reason the writer believes there 
was very little shifting of interest other than such as was due to 
the distraction accompanying fatigue. 

For the group curves obtained from the absolute measures (See 
Table IX) the maximum of attempts was reached, in the case of the 
Third and Fourth grade group, in the tenth period or between the 
eighteenth and twentieth minutes. The maximum of accurates 



ATTEMPTED AND ACCURATE PERFORMANCE 1J 

occurred in the third period or at about the sixth minute. As to 
the minima, they occur before the maxima and indicate lack of 
adaptation in consequence. The foregoing facts indicate that the 
maximum was reached earlier by fourteen minutes in the accurates 
curve than in the attempts curve. For the similar curves of the 
Seventh and Eighth grade group the same observation is made that 
the maximum of accurates preceded that of attempts by ten min- 
utes. The older group showed more persistence, as the maximum 
of accurates occurred in the ninth period or about the eighteenth 
minute and that of attempts in the fifteenth period, or between 
the twenty-eighth and thirtieth minutes. Oehrn found that when 
his adult subjects added continuously for two hours, they attained 
their maximal speed about twenty-eight minutes from the start. 
(Whipple, Manual of Mental and Physical Tests, 335.) 

From the curves representing the average of the individual 
curves the same thing is true as to the maximal attainment of 
accuracy occurring before that of work in attempts. The minima 
of accuracy since they are found following the maximal points in 
both groups register fatigue. (See Table X for the data from which 
these observations are made.) 

The two standpoints — interest in total work and in changes in 
working ability — make practically no difference as to the time of 
occurrence of the maxima. 

The general conclusions to be drawn here are then: 

1. Fatigue is made evident in a curve of this sort by the line falling away 
from the maximum. 

2. Workers attain their maximum of accuracy before they attain that 
point in attempting. 

3. In both quantity and quality of work, the younger children reach 
their maximum as a group before the older ones, and therefore notably 
fatigue sooner. 

4. The occurrence of the minimum after the maximum is in consequence 
of fatigue and not from lack of adaptation. 

Fatigue 

If we wish to find fatigue in an attempt or accurate performance 
curve we look for it certainly at the end of the performance because, 
though it may have been a factor nearly all along the way, it would 
here be more in evidence than elsewhere. Fatigue is made evident 



10 MENTAL FATIGUE DURING CONTINUOUS EXERCISE 

by a falling away from a previous performance. Now we must 
have something to measure by as well as something to measure. 
The basis of measurement or comparison taken here is the average 
of the first three periods of work. By taking our standard at the 
beginning we avoid practice and fatigue effects. 

The question of novelty of stimulus is of slight importance here 
since the subjects were rather familiar with such material as that 
given in the experiment. 

That part of the data of Tables IX and X given as III and IV, 
'average of first three' and 'average of last three', forms the mea- 
sures which are compared for the purpose of ascertaining the fatigue 
at the end of the total time of working. 'Average first three' sig- 
nifies the average of the first three periods of two minutes each, 
and the average of the last three periods of two minutes each is sig- 
nified by 'last three'. The facts under III give the basis of compari- 
son. V, 'per cent, of loss or gain', indicates the results of the com- 
parisons for the various curves. The results show that in abso- 
lute measures attempts gained slightly and accurate performance 
lost. The gain for attempts of Third and Fourth grade group was 
2 per cent., for Seventh and Eighth grades, I per cent. The fatigue 
in accurates of Third and Fourth grade groups was 6.2 per cent, and 
for Seventh and Eighth grades was 7 per cent. 

The result of similar comparisons in Average of Individual Curves 
made after the same fashion as that of Absolute Measures shows 
there was fatigue in both attempts and accurates in both the 
younger and the older groups. (See Table X.) Fatigue in attempts 
for the former was 3 per cent., for the latter was 4 per cent., but the 
accurates suffered a 17 per cent, loss for the younger group and 
10.2 per cent, for the older. 

If the writer's contention is accepted that the curves represent- 
ing the Average of the Individual Curves best represent the facts, 
we may conclude that attempts and accurates alike suffer fatigue 
in an exercise of this sort. 

General Form of the Curves 

We first present Figures i-a,2-a,3-a and 4-a, which are "smoothed" 
from Figures 1, 2, 3 and 4 respectively, by taking the averages of 
the first and second periods, of the third and fourth, etc.; i. e., the 
two-minute periods of the experiment are here combined into units 



ATTEMPTED AND ACCURATE PERFORMANCE 



19 



of four minutes each. Some of the chance irregularities of the origi- 
nal curves being thus removed, the general course of the curves can 
be better seen. 

From Figures i-a and 2-a it appears that the working power of the 
group as a whole remained very nearly constant during the experi- 






J L 



J L 



Periods 2 4 6 8 10 12 

Fig. i-a. Third and Fourth Grades 



14 



I 3 

U 



ffccurttes 



-t 1 1 u 



Periods 2 4 6 8 10 12 14 16 18 20 

Fig. 2-a. Seventh and Eighth Grades 



20 



MENTAL FATIGUE DURING CONTINUOUS EXERCISE 



ment, though there is a slight but definite descent in the curves for 
accurate work, and this decline begins earlier in the younger than 
in the older group. 





8 


■■» 


»" 
* 


*"*^ 




7 


' 








6 


* 








5 








en 










c 
u 
u 
u 
1) 

il 


4 
3 

2 
I 


t 1 




— 1 u 



**«* 






Periods 



46 8 10 

-F*g> J-o. Third and Fourth Grades 



H 



We next divide the curves into three parts, as nearly as possible 
thirds in the Third and Fourth group, and exact thirds in the 
Seventh and Eighth grade group. The former group is divided 
thus — four periods in the first part and five periods in the second 
and third parts. The fact that there were fourteen periods makes 
this unequal division necessary. The Seventh and Eighth grade 
group curve is divided into three parts, each containing seven 



ATTEMPTED AND ACCURATE PERFORMANCE 21 

periods. In the accompanying table, No. IX, for Group Curves, 
if the reader will refer to VI, VII, and VIII, he will find the averages 
and ratios to which we are going to refer. In the case of the Third 
and Fourth grade group the average amount attempted each two 
minutes for this part of the curve (eight minutes) was 3.36 columns, 
for the second part or ten minutes following the first division of 
time, the average was 3.44 columns and for the last ten minutes of 

6 r 



o 3 

<u 

Oh 






Periods 246 8 10 12 14 ib 18 20 

Fig. 4-a. Seventh and Eighth Grades 

work 3.45 columns were attempted for two minutes on the average. 
This shows a steady rise, in the ratios of 1.00, 1.023, an d 1.026. 

In the case of the Seventh and Eighth grade group the three 
equal parts of the whole forty-two minutes show thus an average 
for the first fourteen minutes of 5.74 columns attempted, for the 
second fourteen minutes 5.84 columns were attempted and for the 
last fourteen minutes of time an average of 5.97 columns were at- 
tempted for two minutes. This likewise shows a rise. The ratios 
are 1.00, 1.017, and 1.04. These rises are so slight that too much 
significance should not be given them. 

In the case of accurates, the first eight minutes in the Third 
and Fourth grade groups shows an average of 1.95 columns correctly 
solved for each two minutes. The next ten minutes of the total 
time produced an average of 1.96 columns correctly solved for each 



22 MENTAL FATIGUE DURING CONTINUOUS EXERCISE 

two minutes and the last ten minutes shows an average of 1.86 
columns per period of two minutes each, correctly added. The 
ratios are 1.00, 1.005, and .95. With the older groups the three 
averages are 4.14, 4.20, and 4.01. The ratios are 1.00, 1. 014, and .97. 

The accurate performance curves here are seen to rise in the 
middle and decline at the end, but the attempts curves rise steadily 
in both groups. Practice was helping out very much in this, for 
them, quasi-automatic process. 

Therefore, taking the group curves in three parts as we have 
just done shows (1) slight practice effect in the attempts process in 
both groups, (2) slight practice effect in the accuracy curve in the 
second third of the partition of the curve but fatigue in the last 
third in both groups, all of which holds alone for the absolute 
measures. 

The above facts hold for the curves derived from absolute mea- 
sures, but the corresponding parts of the curves showing average 
of the individual curves are somewhat different in their relations. 

The numbers in the curves are these (See Table X) : 

Third and Fourth Third and Fourth 

Grades Attempts Grades Accuracy 

First Third, as base 1 . 00 First third as base 1 . 00 

Second third : first third . 99 Second third : first third . 98 

Third third : first third .q8 Third third : first third .88 



Seventh and Eighth Seventh and Eighth 

Grades Attempts Grades Accuracy 

First third as base 1 . 00 First third as base 1 . 00 

Second third : first third . 96 Second third : first third . 99 

Third third : first third 1 . 004 Third third : first third . 95 

The result is accordingly that the average individual falls off 
slightly in work attempted, with some recovery toward the end 
in the case of the older individuals (Seventh and Eighth grades) ; 
while in accurate work, the average individual shows a greater 
falling off, without recovery, and the falling off is greater in the 
younger child. The conclusion from this form of comparison is in 
general harmony with that derived from the immediately preceding 
comparison and with that derived from inspection of the curves. 



ATTEMPTED AND ACCURATE PERFORMANCE 23 

'Warming-iip' and l Initial-Spur? 

We now proceed to examine these curves to see if there is 'Warm- 
ing-up' or 'Initial-spurt'. "The best definition of 'Warming-up' as 
an objective act is that part of an increase of efficiency during the 
first twenty minutes (or some other assigned early portion) of a 
work period, which is abolished by a moderate rest, say of sixty 
minutes." Thorndike, Educational Psychology, vol. Ill, p. 66. 
"'Initial-spurt', if a real fact, will be found in an examination of 
the work, minute by minute, of the first quarter of an hour." Ibid., 
p. 48. A sudden rise at the start will indicate 'Initial-spurt'. 

The graphic representation of the attempted and accurate work 
affords perhaps the best objective material for determining the 
presence or absence of these phenomena in the performance under 
discussion, and so we call attention to the curves given in Figures 
1 and 2, and derived from Tables I, II, III, and IV for Absolute 
Measures, and Figures 3 and 4 derived from Tables V, VI, VII, 
and VIII. The curves for the younger group show a fairly steady 
rise in the first six minutes in both attempts and accurate perfor- 
mances in all the curves representing them, and from this evidence 
we may say there was 'Warming-up' for them. If it should be 
objected that these rises were merely incidental and due to chance, 
we may resort to the tables showing the averages and their probable 
errors. By taking the difference between the averages of the suc- 
cessive periods, first and second, second and third, and bringing 
these into relation to the square root of the sum of their respective 
squared P. E.'s, we may determine the reliability of these differences. 
We give here these reliabilities. The chances that the gain of period 
two over period one, in Table I, is reliable are 91 out of 100; for peri- 
od three over period two they are 75 out of 100. This 'Warming-up' 
holds there for attempts in the Third and Fourth grades. As to 
accurates the case is even better, for the chances that the gain of 
period two over period one, in Table II, is reliable are 96 out of 100, 
and of the gain of period three over period two are 92 out of 
100, in the Third and Fourth grades. This holds for the Absolute 
Measures. 

In the case of the curves representing the Average of the Indi- 
vidual Curves, we have the following facts as to 'Warming-up'. 
The chances that the gain of period two over period one is a true 



24 MENTAL FATIGUE DURING CONTINUOUS EXERCISE 

one are 87 out of 100. The chances that the gain of the third period 
over the second period (Table V) is significant are not so great, 
being only 32 out of 1 00 cases. In Table VI the gain of second 
period over the first, has a reliability of 84 cases out of 100. But 
there is no gain of the third period over the second, so that the 
'Warming-up' disappeared by the time the sixth minute was 
reached. 

Therefore, we may conclude, since the rise in the curves is found 
to be more or less reliable, that the 'Warming-up' found at the 
beginning of the work of the younger group was a real fact. 

Now if there is here found in the younger group positive evidence 
of 'Warming-up', the fact excludes the possibility of 'Initial-spurt', 
which is in a measure the opposite of 'Warming-up'. 

The curves for the older group do not show a 'Warming-up 'effect 
upon inspection. The rather sudden slight rise in the first period, 
followed by a fall in the second period, on the face of things indi- 
cates 'Initial-spurt' in both attempted and accurate performance. 
If we examine periods one and two (Table III) and take into account 
their probable errors we find that the loss of the second period over 
the first, has a reliability as a change of 98 out of 100 cases. This is 
for attempts. For accurates we take periods one and two, with 
their probable errors (Table IV), and find that the loss here is a 
difference whose reliability is 82 chances out of 100. These tables 
give the data for the Absolute Measures. The data for the curves 
representing the average of the Individual curves is found in 
Tables VII and VIII for attempts and accurates respectively. For 
attempts the chances that the change in going from the first period 
to the second is a real fact are 88 out of 100 cases and for accurate 
performances are 74 out of 100. The indications of 'Initial-spurt' 
are found thus to be fairly reliable. 

Therefore, in so far as these data are concerned, the older chil- 
dren experienced an 'Initial-spurt' which is opposite to the 'Warm- 
ing-up' experienced by the younger ones. 

'End-Spurt' 

Since the experiment was planned so as to avoid anything like 
'End-spurt' and let fatigue do its worst at the end, it hardly seems 
worth while to examine these data with the intention of finding 
'End-spurt', which, according to Kraepelin and others, is a sudden 



'"" MPaawMM^ BPBMHg^MBBB 



ATTEMPTED AND ACCURATE PERFORMANCE 25 

rise in efficiency, due to a knowledge on the part of the subjects of 
the approaching end of the task. 

The experimenter here did all in his power to conceal the ap- 
proaching end of the test. For this reason we do not think these 
data should be examined with the end in view of finding 'End-spurt'. 

The writer has a conviction that interference operated at the be- 
ginning of the test because of the strong motivation. The desire 
to excel must have acted as a hindrance at this part of the game in- 
asmuch as it probably acted as a distraction from letting the nec- 
essary associations play freely. Consequently, it would lower the 
score especially of accuracy. It also probably played strongly 
toward the end of the test and may account for some of the fatigue. 



CHAPTER III 
INDIVIDUAL DIFFERENCES 

Individual Curves 

In the preceding chapter, individual differences were eliminated 
and the general tendencies to fatigue, etc., of large groups alone 
considered. If we take the records of individuals, we shall, of 
course, find every variety of curve. Some do most of their work 
at the start and show fatigue considerably towards the end, some 
work steadily from start to finish, and some improve all the way. 
Such differences may be due to slight intercurrent causes, and are 
not, in the lack of further evidence, to be regarded as indicative of 
different types of workers. It may be well, however, to present 
the records of a few individuals, selected more or less at random 
from among those whose total performance was small, medium, or 
great. The data given in Table XI show for each individual the 
per cent, of his total accomplishment done in each successive period 
of two minutes. Data are given for twenty individuals in all, ten 
from the Third and Fourth grades and ten from the Seventh and 
Eighth, five in each group showing the results for attempts and five 
for accurate work. 

For example, Case 22 from the Third and Fourth grade group 
attempted twenty-one columns in all, twenty- three per cent, of 
these being attempted in the first three periods, sixty-one per cent, 
in the first half of the time, and only nineteen per cent, in the last 
three periods— showing thus a considerable falling off in energy 
towards the end. Case 367, on the contrary, attempted only four- 
teen per cent, of his total of one hundred and ninety-one columns 
in the first three periods, forty-six per cent, in the first half of the 
time, and twenty-four per cent, in the last three periods. 

These differences are found all along the way in going from the 
poorest total performance to the best. Some poor in total perfor- 
mance are steady workers. Some enthusiastic workers at the start 
do not do so well at the end, but do well in total performance. 
Those workers who profit by practice are found among the poorer 



INDIVIDUAL DIFFERENCES 



27 



workers as well as among the better workers as determined by total 
performances. 



TABLE XI 

Showing Changes in Working Ability — Third and Fourth Grades 
Per Cent, of Columns Attempted 



Period 



Case 22 
Per Cent. 



Case 138 
Per Cent. 



Case 276 
Per Cent. 



Case 344 
Per Cent. 



Case 367 
Per Cent. 



14 

5 



33 



23 



15 



14 



o 

14 

9 

5 



61 



7 
10 

5 



53 



39 



50 



46 



8 

9 
10 
11 



12 

13 
14 



100 19 



100 19 



100 26 



100 24 



Average 
per cent. 

Total columns 
attempted 



7-1 



7-i 



40 



7-1 



60 



7-1 



79 



7-1 



191 



28 MENTAL FATIGUE DURING CONTINUOUS EXERCISE 

TABLE XI (Continued) 

Third and Fourth Grades — Per Cent, of Total Accurate Columns 

Case J2g Case 350 Case 368 

Per Cent. Per Cent. Per Cent. 





Case 142 


Co.se 246 


•riod 


Per Cent. 


Per Cent. 


1 


26 


15 


2 


16 


15 


3 


11 


9 



4 


11 


9 


10 


5 





3 


5 


6 








8 


7 


10 


9 


8 



8 7 4 

8 7 7 

697 

53 39 22 23 



74 60 53 51 48 



8 5 15 8 7 6 

9 11 4 5 6 9 

10 o 12 8 8 8 

11 50656 

12 00698 

13 5 9 8 7 8 

14 00877 

IOO 5 100 9 100 22 100 23 100 23 

Average 

per cent. 7.1 7.1 7.1 7.1 7.1 

Total accurate 

columns 19 33 50 60 no 



EBMB— n mM«MiunMMMMmimm««i 



INDIVIDUAL DIFFERENCES 29 

TABLE XI {Continued) 

Seventh and Eighth Grades — Per Cent, of Columns Attempted 

Case 32 Case 52 Case 215 Case 2q8 Case 336 

Period Per Cent. Per Cent. Per Cent. Per Cent. Per Cent. 

1 84345 

2 66254 

3 5 3 3 5 4 

19 13 8 14 13 



5 


6 


6 


2 


4 


5 


6 


6 


6 


1 


5 


4 


7 


5 


4 


3 


6 


4 


8 


5 


6 


3 


6 


4 


9 


6 


4 


4 


4 


4 


10 


4 


3 


4 


5 


4 


11 


4 


3 


6 


5 


4 



60 48 34 55 47 

12 36745 

13 66844 

14 4 4.8 5 4 

15 53644 

16 53644 

17 46654 

18 36644 

19 36544 

20 36554 

21 36464 

100 9 100 18 100 14 100 15 100 12 



Average 

percent. 4.7 4.7 4.7 4.7 4.7 

Total columns 

attempted 77 89 133 160 223 



30 MENTAL FATIGUE DURING CONTINUOUS EXERCISE 

TABLE XI (Continued) 
Seventh and Eighth Grades — Per Cent, of Total Accurate Columns 





Case 20 


Case 64 


Case 208 


Case 304 


Case 343 


riod 


Per Cent. 


Per Cent. 


Per Cent. 


Per Cent. 


Per Cent. 


i 


IO 


10 


2 


5 


4 


2 


IO 


10 


5 


5 


4 


3 


12 


4 


2 


5 


5 



32 24 9 15 13 



4 


7 


6 


3 


5 


6 


5 


5 


6 


6 


4 


4 


6 


3 


6 


6 


5 


5 


7 


5 


4 


3 


4 


4 


8 


7 


8 


6 


5 


4 


9 








3 


4 


5 


10 


3 


6 


6 


5 


4 



62 58 42 47 45 



II 


5 


4 


6 


4 


6 


12 


O 


4 


6 


5 


4 


13 


3 


5 


3 


5 


6 


14 


3 


3 


5 


5 


5 


15 


3 


4 


5 


5 


5 


16 





2 


6 


5 


4 


17 


4 


4 


5 


5 


5 


18 


5 


2 


5 


4 


6 


19 


3 


4 


5 


5 


6 


20 


5 


6 


6 


5 


4 


21 


7 


4 


6 


6 


4 



100 15 100 14 100 17 100 16 100 14 



Average 

percent. 4.7 4.7 4.7 4.7 4.7 

Total of accu- 
rate columns 40 52 88 135 242 



m»¥inmrrrnTTrnmrfirmrmnninnnnnimn 



I^KnHnaNHH^HHBBIHHHHBBHI 



INDIVIDUAL DIFFERENCES 



31 



Fatigue As Related to Total Performance 

The purpose of this manner of handling the materials of the 
experiment is to see whether the work curve would be the same for 
those who accomplish much and for those who accomplish little 
in the total time; or whether the better workers fatigue more or 
less rapidly than the poorer workers. 



Third ondTourtb Grade Qnoup divided into Tenths 




P&r/oc/o 



ri^.5~ Accu ndfeS 



The two groups are divided into sub-groups on the basis of the 
total amount done in twenty-eight and forty-two minutes respec- 
tively. The 368 children of the Third and Fourth grades were 
arranged in rank order from lowest to highest, according to the 
total attempted in the twenty-eight minutes, and again according 
to the total accurate in the twenty-eight minutes, and this rank 
order arrangement was cut into ten parts. Each tenth of the 368 
makes a sub-group, the sub-groups running from lowest to highest 
or upper tenth. The average of each sub-group was determined 
and curves were formed for these ten sub-groups. There are twenty 



32 



MENTAL FATIGUE DURING CONTINUOUS EXERCISE 



curves for the Third and Fourth grades. Likewise, there are 
twenty curves for the Seventh and Eighth grades. The 343 chil- 
dren in this group were arranged in rank order from lowest to 



i 




>c/*J* 



J L 



J L 



J L 



Ft fr ~& - At t* npfs. 



highest tenth or upper tenth, as in the case of the Third and Fourth 
grades and the numbers were treated in the same way. 

These curves are handled in much the same way as the larger 
group curves. The idea here is to see if there is any difference in 
the form of a curve for a poor total accomplishment from that of 
the better accomplishment. 



INDIVIDUAL DIFFERENCES 



33 






T 



H NHfttfJfN ^H 



^ 

&* 

* 



1? 

■8' 

ft 




34 



MENTAL FATIGUE DURING CONTINUOUS EXERCISE 



//t*.m 



X to w 



C */">** J /7cci4rat^ 



0) 



Tn — i i i . i — i — r 



V » 4 **/ / / / / 

\ » / 1 / ^ / / / -/ 



< ( - H W 1 



>\ i 



> 



>l 



> 



/ 



>/ 6 ( > ) > / 

\ < * < ) v o v 

V>Yy'< > \ 

c < <YfY<f< <^ 



i S>V»>> 



> 



- ) /< ?« \< 

- > ilk* ( 

I \ J / l\ ) \ 1 



f 



) ( 



I 



ri 



Co 



OQd 


(A 



I 






INDIVIDUAL DIFFERENCES 



35 



TABLE XII 

Attempts of Third and Fourth Grades 

The 368 cases are divided into ten groups on the basis of total amount 

done in twenty-eight minutes, going from lowest tenth to 

upper tenth. Below are given the averages for each 

First (Lowest) Tenth — 37 Cases 



'erio 


d Average / 


.D. 


P.E 


1 


152 


75 


.11 


2 


1 


5 


63 


.09 


3 


1 


27 


59 


.08 


4 


1 


19 


59 


.08 


5 


1 


44 


56 


.08 


6 


1 


36 


67 


.09 


7 


1 


22 


49 


.07 


8 


1 


33 


60 


.08 


9 


1 


22 


42 


.06 


10 


1 


36 


61 


.09 


11 


1 


22 


46 


.06 


12 


1 


33 


5i 


.07 


13 


1 


38 


59 


.07 


H 


1 


08 


39 


•05 




Third Tenth — k 


?7 Cases 


erio 


d Average A 


.D. 


P.E. 


1 


2-43 


7i 


. 1 


2 


2.29 


64 


.09 


3 


2-49 


58 


.08 


4 


2-37 


54 


.08 


5 


2.4 


6 


.09 


6 


2.52 


49 


.07 


7 


2.27 


54 


.07 


8 


2.4 


56 


.08 


9 


2-45 


58 


.08 


10 


2.29 


53 


.07 


11 


2-37 


55 


.07 


12 


2.02 


47 


.07 


13 


2.21 


29 


.04 


14 


2 


08 


6 


.08 



Second Tenth — 


37 Cases 


Period 


Average / 


.D. 


P.E 


1 


1.84 


55 


.08 


2 


1.98 


4i 


.06 


3 


1.98 


3i 


•03 


4 


1.87 


4i 


.06 


5 


1.76 


5i 


.08 


6 


1.82 


46 


.06 


7 


2.0 


27 


. 1 


8 


1-9 


42 


.06 


9 


1.92 


5 


.07 


10 


2.05 


45 


.06 


11 


2.05 


3 


.04 


12 


1.85 


46 


.06 


13 


2.02 


36 


•05 


14 


2.08 


6 


.08 


Fourth Tenth — 37 Cases 


Period 


Average / 


[.D. 


P.E 


1 


2-43 


66 


.09 


2 


2.92 


55 


.08 


3 


3.16 


47 


.07 


4 


2.84 


6 


.08 


5 


2.63 


61 


.09 


6 


2-79 


54 


.08 


7 


2-43 


6 


.08 


8 


2.76 


47 


.07 


9 


2.79 


56 


.08 


10 


2.9 


47 


.07 


11 


3.02 


52 


.08 


12 


2.71 


79 


. 11 


13 


2-73 


54 


.08 


H 


2.71 


59 


.08 



36 



MENTAL FATIGUE DURING CONTINUOUS EXERCISE 



TABLE XII (Continued) 
Attempts of Third and Fourth Grades 



Fifth Tenth — 37 Cases 



Period 


Average /. 


.D. 


P.E 


1 


2-95 


88 


.12 


2 


3 


4i 


5 


.07 


3 


3 


29 


45 


.06 


4 


3 


24 


5i 


.07 


5 


3 


05 


46 


.06 


6 


3 


35 


59 


.08 


7 


3 




37 


•05 


8 


3 


1 


52 


.07 


9 


3 


05 


46 


.06 


10 


3 


32 


58 


.08 


11 


3 


13 


51 


.07 


12 


2 


92 


5 


.07 


13 


3 


21 


54 


.08 


14 


3 


05 


75 


. 10 



Seventh Tenth — 37 Cases 
Period Average A. D. P.E. 



I 


3 


37 


76 


.11 


2 


3 


86 


61 


.09 


3 


3 


92 


40 


.06 


4 


3 


86 


53 


.07 


5 


3 


57 


62 


.09 


6 


3 


98 


4i 


.06 


7 


3 


92 


62 


.09 


8 


4 


05 


46 


.06 


9 


4 


18 


5 


.07 


10 


4 


16 


52 


.07 


11 


4 


05 


46 


.06 


12 


3 


87 


55 


.08 


13 


4 


02 


47 


.07 


14 


4 


05 


46 


.06 



Sixth Tenth — 37 Cases 



Period 


Average /. 


.D. P.E. 


1 


3-43 


79 


11 


2 


3 


64 


68 


10 


3 


3 


7 


58 


08 


4 


3 


79 


50 


07 


5 


3 


43 


59 


08 


6 


3 


62 


52 


07 


7 


3 


5i 


58 


08 


8 


3 


57 


6 


08 


9 


3 


64 


56 


08 


10 


3 


37 


65 


09 


11 


3 


45 


68 


10 


12 


3 


27 


55 


08 


13 


3 


76 


61 


09 


14 


3 


32 


76 


10 


Eighth Tenth — 


37 Cases 




Period 


Average / 


. D. P. E. 


1 


4.29 


85 


12 


2 


4 


02 


69 


10 


3 


4 


34 


64 


09 


4 


4 


29 


64 


09 


5 


4 


16 


56 


08 


6 


4 


40 


63 


09 


7 


4 


13 


67 


10 


8 


4 


56 


79 


11 


9 


4 


64 


75 


10 


10 


4 


29 


79 


11 


11 


4 


32 


61 


09 


12 


3 


94 


67 


093 


13 


4 


16 


64 


089 


14 


4 


34 


93 


132 



INDIVIDUAL DIFFERENCES 



37 



TABLE XII (Continued) 
Attempts of Third and Fourth Grades 



Ninth Tenth— j 6 Cases Tenth Tenth 


— 36 Cases 


Period Average /. 


. Z). P. £. Period Average 


A.D. P.E 


I 4.21 


85 .12 1 5.16 


1 


18 .17 


2 4 


61 


71 .10 2 5.75 


1 


11 .16 


3 4 


58 


79 -ii 3 6.05 


1 


13 -16 


4 5 


22 


65 .09 4 6.25 


1 


13 .16 


5 4 


62 


61 .09 5 5.78 


1 


22 .17 


6 4 


89 


50 .07 6 5.39 


1 


09 -15 


7 4 


81 


65 .09 7 6.61 


1 


57 -22 


8 4 


95 


58 .08 8 6.58 


1 


47 -20 


9 4 


78 


72 .10 9 6.92 


1 


60 .22 


10 5 


36 


7 .10 10 6.75 


1 


56 .22 


11 5 


00 


55 08 11 6.36 




94 -13 


12 4 


64 


73 .10 12 6.52 


1 


42 .20 


13 4 


78 


67 .09 13 6.41 


1 


48 .20 


14 4 


44 


78 .11 14 6.70 
TABLE XIII 


1 


44 .20 



Accurates of Third and Fourth Grades 

The 368 cases are divided into ten groups on the basis of total amount 

done in twenty-eight minutes, going from lowest tenth to upper 

tenth. Below are given the averages for each group 

First (Lowest) Tenth— 37 Cases 



erioO. 


Average /. 


.D. 


P.E 


1 


• 13 


26 


.04 


2 


•36 


49 


.06 


3 


.27 


40 


.06 


4 


.24 


36 


■05 


5 


.29 


43 


.06 


6 


•32 


43 


.06 


7 


.21 


34 


•05 


8 


.16 


27 


.04 


9 


.40 


56 


.08 


10 


.21 


34 


•05 


11 


.21 


34 


•05 


12 


.21 


33 


•05 


13 


. .24 


52 


.08 


H 


.18 


3i 


.04 





Second Tenth — 


37 Cases 


zrio 


i Average / 


LD. 


P.E 


1 


•37 


56 


.08 


2 




81 


77 


.11 


3 




81 


65 


.09 


4 




5i 


58 


.08 


5 




67 


58 


.08 


6 




70 


57 


.08 


7 




78 


59 


.08 


8 




59 


57 


.08 


9 




48 


52 


.08 


10 




72 


67 


.09 


11 




40 


54 


.08 


12 




59 


67 


.09 


13 




62 


60 


.08 


14 




43 


58 


.08 



38 



MENTAL FATIGUE DURING CONTINUOUS EXERCISE 



TABLE XIII (Continued) 
Accurates of Third and Fourth Grades 



Third Tenth — 37 Cases 
Period Average A. D. P.E. 



I 




59 


64 


.08 


2 


1. 18 


81 


.11 


3 


1 13 


58 


.08 


4 


1. 00 


7 


.1 


5 


1.05 1 


3 


.18 


6 


•9i 


59 


.08 


7 


•75 


65 


.08 


8 


1.08 1 


00 


.14 


9 


•97 


57 


.08 


10 


.78 


72 


.10 


11 


.82 


60 


.08 


12 


.89 


74 


.10 


13 


.64 


73 


.10 


14 


.86 


56 


.08 




Fifth Tenth — 3 


7 Cases 




Period Average /. 


.D. 


P.E 


1 


1-55 


74 


.10 


2 




7i 


78 


.10 


3 




79 


78 


.10 


4 




79 


77 


.10 


5 




55 


74 


.10 


6 




87 


76 


.10 


7 




43 


66 


.09 


8 




60 


74 


.10 


9 




60 


90 


•13 


10 




45 


79 


.10 


11 




65 


68 


.09 


12 




18 


63 


.09 


13 




68 


61 


.09 


14 




49 


85 


•13 





Fourth Tenth 


— 37 Cases 




Period Average 


A.D. P 


.E 


1 


1 .26 


.82 


11 


2 


1.40 


.83 


n 


3 


i-37 


1.1 


15 


4 


"•43 


.66 


09 


5 


113 


•73 


10 


6 


1.24 


.65 


09 


7 


1 .24 


•7i 


10 


8 


1-43 


•74 


10 


9 


1.05 


•56 


08 


10 


1. 18 


.78 


11 


11 


i-55 


.76 


11 


12 


.72 


.76 


1 1 


13 


1. 21 


•79 


11 


H 


.90 


.67 


09 




Sixth Tenth- 


—37 Cases 




Period 


Average 


A.D. P.E 


I 


1 .90 


1 .04 


15 


2 


1-95 


.88 


12 


3 


2.18 


•9i 


12 


4 


2.00 


.70 


10 


5 


2.08 


.64 


09 


6 


2.29 


.80 


11 


7 


i-95 


•77 


11 


8 


1.87 


1 .01 


14 


9 


1.68 


.80 


1 1 


10 


2.02 


•84 


11 


11 


i-73 


.98 


U 


12 


1.63 


■71 


10 


13 


i-73 


•75 


11 


14 


1.63 


1.03 


14 



INDIVIDUAL DIFFERENCES 



39 



TABLE XIII {Continued) 
Accurates of Third and Fourth Grades 



Seventh Tenth 


— 37 Cases 


Period 


Average 


A.D. 


P.E 


i 


1.89 


.88 


• 13 


2 


2.71 


1 .00 


•14 


3 


2-73 


1.03 


•14 


4 


2-73 


.72 


.10 


5 


1.79 


.61 


.09 


6 


2.52 


.84 


.11 


7 


2.10 


.62 


.09 


8 


2.21 


.83 


.11 


9 


2-44 


.88 


• 13 


10 


2.60 


•79 


.10 


ii 


2.27 


.92 


.12 


12 


2.08 


•9i 


.12 


13 


2-35 


.84 


.11 


H 


2.16 


.80 


.11 



Ninth Tenth — 36 Cases 
Period Average A.D. 



P.E. 



I 


2 


73 


1 .04 


15 


2 


3 


57 


.85 


12 


3 


3 


33 


.88 


12 


4 


3 


63 


.82 


12 


5 


3 


27 


.82 


12 


6 


3 


10 


• 73 


10 


7 


3 


13 


•74 


10 


8 


4 


08 


1.36 


19 


9 


3 


27 


1.05 


15 


10 


3 


16 


.86 


12 


11 


3 


45 


•91 


12 


12 


3 


08 


.82 


12 


13 


3 


40 


•99 


14 


14 


3 


27 


1 .01 


15 



Eighth Tenth — 37 Cases 



Period 


Average 


A.D. P.E 


1 


2.49 


1 .04 


15 


2 


2-79 


1 .02 


H 


3 


316 


•74 


10 


4 


2.98 


•89 


12 


5 


2-79 


.86 


12 


6 


3.00 


.64 


09 


7 


2.68 


.88 


12 


8 


2.82 


1 .01 


H 


9 


3.02 


•79 


10 


10 


2.84 


1 .06 


14 


11 


2-95 


•72 


10 


12 


2.29 


.86 


12 


13 


2-79 


•97 


H 


H 


2.29 


•74 


10 




Tenth Tenth- 


— 36 Cases 




Period 


Average 


A.D. P.E 


1 


3-84 


.96 


13 


2 


4 


5 


1. 16 


16 


3 


4 


78 


1 .02 


15 


4 


4 


4i 


1. 19 


17 


5 


4 


19 


•93 


12 


6 


4 


67 


1. 03 


15 


7 


4 


47 


1 .02 


15 


8 


4 


73 


.82 


12 


9 


4 


89 


• 96 


H 


10 


4 


55 


1.05 


15 


11 


4 


33 


1. 14 


16 


12 


4 


25 


1-34 


19 


13 


4 


08 


1.36 


19 


H 


4 


30 


1 .29 


18 



40 



MENTAL FATIGUE DURING CONTINUOUS EXERCISE 



TABLE XIV 

Attempts of Seventh and Eighth Grades 

The 343 cases are divided into ten groups on the basis of total amount 

done in forty-two minutes, going from lowest tenth to upper 

tenth. Below are given the averages for each group 



First (Lowest) Tenth— -35 Cases 


Period 


Average A 


l.D. P.E 


1 


3-71 1 


13 


16 


2 


3-42 


89 


13 


3 


3-37 


65 


09 


4 


3-66 


87 


12 


5 


3-17 


68 


10 


6 


3-55 


73 


11 


7 


3-17 


61 


09 


8 


3.08 


63 


09 


9 


3.20 


56 


08 


10 


3-40 


57 


08 


11 


3-15 


57 


08 


12 


2.83 


64 


09 


13 


3.22 


55 


08 


14 


309 


68 


10 


15 


2.87 


64 


09 


16 


3-25 


70 


10 


17 


3-31 


77 


11 


18 


306 


70 


10 


19 


3-57 


98 


14 


20 


3-57 


84 


12 


21 


2.86 


65 


09 


Third Tenth — ^ 


]4 Cases 




Period 


Average A 


l.D. I 


\E 


1 


4.88 


76 


09 


2 


4 


74 


62 


12 


3 


4 


83 


68 


11 


4 


4 


68 


57 


12 


5 


3 


88 


53 


11 


6 


4 


68 


57 


07 


7 


4 


21 


69 


11 


8 


4 


77 


68 


09 


9 


4 


7i 


71 


07 


10 


4 


98 


57 


08 


11 


4 


79 


7i 


10 


12 


4 


38 


56 


08 


13 


5 


00 


52 


10 





Second Tenth 


— 35 Cases 


Perio 


d Average 


A.D. 


P.E 


1 


4-65 


1 .24 


■19 


2 


4 


85 


.89 


•13 


3 


4 


00 


■74 


.10 


4 


4 


14 


•63 


.09 


5 


4 


88 


1 .02 


.14 


6 


4 


20 


.60 


.09 


7 


3 


95 


•50 


.07 


8 


4 


00 


.80 


.12 


9 


4 


11 


.61 


.09 


10 


4 


33 


•58 


.08 


11 


4 


22 


•73 


.10 


12 


3 


83 


.48 


.07 


13 


4 


17 


.80 


. 12 


14 


3 


8 


.67 


. 10 


15 


4 


34 


.84 


. 12 


16 


4 


3i 


•83 


.11 


17 


4 


58 


■72 


.10 


18 


4 


11 


.82 


. 12 


19 


3 


75 


.67 


.10 


20 


4 


3i 


•85 


. 12 


21 


4 


85 


1.05 


•15 




Fourth Tenth 


— j 4 Cases 


Period Average 


A.D. 


P.E 


1 


4.89 


1.03 


■14 


2 


4 


86 


•5i 


.07 


3 


4 


94 


.66 


■19 


4 


5 


21 


■57 


.08 


5 


4 


74 


•63 


.09 


6 


5 


11 


■73 


.10 


7 


5 


02 


■51 


.07 


8 


4 


94 


.67 


. 10 


9 


5 


00 


.70 


. 10 


10 


5 


06 


•78 


. 11 


11 


5 


06 


•50 


.07 


12 


5 


16 


.80 


.11 


13 


5 


52 


1 .09 


■15 



INDIVIDUAL DIFFERENCES 



41 



TABLE XIV (Continued) 
Attempts of Seventh and Eighth Grades 



Third Tenth — 34 Cases 



Period 


.4 verage 


A.D. . 


P.E. 


14 


4-17 


.63 


.10 


15 


4 


62 


•75 


.10 


16 


4 


74 


•49 


.08 


17 


4 


77 


.76 


.08 


18 


4 


65 


.86 


.08 


19 


4 


44 


.72 


. 10 


20 


4 


83 


.86 


.09 


21 


3 


59 


.61 


.11 




Fifth Tenth- 


-34 Cases 




Period 


Average 


A.D. 


P.E 


1 


5-53 


i-34 


•19 


2 


5 


09 


.86 


. 12 


3 


5 


4i 


.69 


.10 


4 


5 


62 


■75 


. 11 


5 


4 


97 


.86 


.12 


6 


5 


59 


.67 


.10 


7 


5 


05 


.72 


.10 


8 


5 


53 


•73 


.11 


9 


5 


68 


.62 


.09 


10 


5 


89 


.86 


.12 


11 


5 


68 


.83 


. 12 


12 


5 


45 


.64 


.09 


13 


5 


7i 


•75 


.11 


14 


5 


38 


.62 


.09 


15 


6 


29 


1. 18 


•17 


16 


5 


74 


.84 


.12 


17 


5 


7i 


.70 


.10 


18 


5 


45 


.72 


.10 


19 


4 


42 


1 .06 


• 15 


20 


5 


17 


1 .04 


•15 


21 


5 


38 


.81 


. 12 


Seventh Tenth 


— 34 Cases 


Period 


Average 


A.D. 


P.E 


1 


6.26 


1. 00 


•H 


2 


6. 17 


•75 


.11 


3 


6.32 


.92 


•13 


4 


6.26 


.70 


.10 


5 


5 


74 


.67 


.10 



Fourth Tenth — 34 Cases 
Period Average A.D. P.E. 



14 


5 


17 


80 


12 


15 


5 


26 


85 


12 


16 


5 


29 


86 


12 


17 


5 


21 


67 


19 


18 


4 


12 1. 


04 


15 


19 


4 


53 


99 


14 


20 


5 


23 1. 


11 


16 


21 


4 


86 


69 


10 




Sixth Tenth — 35 Cases 




Period 


Average A 


D. P.E 


1 


5-98 1 


29 


19 


2 


5-75 


62 


09 


3 


5-89 


73 


11 


4 


5-8o 


58 


08 


5 


5-52 


75 


.11 


6 


5-92 


63 


.09 


7 


5-72 


94 


.14 


8 


5-92 


84 


.12 


9 


5-63 


56 


.08 


10 


6.08 


85 


.12 


11 


5-92 


48 


.07 


12 


5-89 


56 


.08 


13 


6.02 


49 


.07 


14 


6.20 


68 


.10 


15 


6.22 1 


06 


•15 


16 


5-78 


68 


. 10 


17 


5-92 


74 


.11 


18 


6.17 


83 


.12 


19 


5-8o 


58 


.08 


20 


6.36 


90 


• 13 


21 


6.22 


74 


.11 




Eighth Tenth — < 


4 Cases 




Period 


Average A 


.D. P.E 


1 


7.29 


98 


• 13 


2 


6.68 


92 


• 13 


3 


6.77 


59 


.08 


4 


6-95 


72 


. 10 


5 


6. 


*i 


62 


.09 



42 



MENTAL FATIGUE DURING CONTINUOUS EXERCISE 



TABLE XIV (Continued) 
Attempts of Seventh and Eighth Grades 



Seventh Tenth — 34 Cases 



Period 


Average A 


D. T 


.E 


6 


6.38 


86 


12 


7 


6-33 


74 


11 


8 


6-35 


84 


12 


9 


5-92 


52 


07 


10 


6.23 


81 


12 


11 


6.32 


77 


11 


12 


6.00 


76 


II 


13 


6.48 


88 


13 


14 


6.98 


97 


14 


15 


7.23 1 


14 


16 


16 


6.44 


87 


13 


17 


6.58 


93 


13 


18 


6.41 


72 


10 


19 


5-68 


86 


12 


20 


6.26 1 


19 


17 


21 


6-35 1 


02 


15 


Ninth Tenth— 3 


4 Cases 




Period 


Average A 


D. I 


'. E 


1 


7-83 1 


13 


16 


2 


6 


83 


93 


13 


3 


7 


59 


78 


11 


4 


7 


50 


79 


11 


5 


7 


H 


7i 


10 


6 


7 


29 


59 


08 


7 


7 


41 


83 


12 


8 


7 


76 


92 


13 


9 


7 


26 


69 


10 


10 


7 


65 


82 


12 


11 


7 


74 


78 


11 


12 


7 


25 


78 


11 


13 


7 


62 


79 


11 


H 


7 


45 


88 


13 


15 


8 


27 1 


48 


21 


16 


7 


02 


62 


09 


17 


6 


77 


79 


11 


18 


7 


28 1 


05 


15 


19 


7 


29 1 


01 


14 


20 


7 


92 


65 


09 


21 


8 


14 1 


25 


18 



Eighth Tenth — 34 Cases 
Period Average A. D. P. E. 



6 


6 


62 


.62 


09 


7 


6-45 


.65 


09 


8 


7-05 


.66 


10 


9 


6.71 


•59 


08 


10 


6.80 


.61 


09 


11 


6.83 


.61 


09 


12 


6-59 


.64 


09 


13 


6.74 


.62 


09 


14 


6.38 


•99 


14 


15 


7-55 


1 .00 


14 


16 


6-95 


•78 


11 


17 


7.21 


.89 


13 


18 


6.69 


.78 


11 


19 


6.62 


.70 


10 


20 


7-05 


.78 


11 


21 


6.92 


•98 


14 




Tenth Tenth- 


— 34 Cases 




Period 


Average 


A.D. P.E 


1 


9.29 


1 .26 


18 


2 


8 


61 


115 


17 


3 


8 


86 


1. 18 


17 


4 


9 


44 


i-3i 


19 


5 


8 


92 


1-39 


20 


6 


8 


89 


1 .09 


16 


7 


8 


98 


115 


17 


8 


8 


95 


1 .12 


16 


9 


8 


83 


1 .04 


15 


10 


9 


38 


1-25 


18 


11 


9 


27 


1.30 


19 


12 


9 


52 


1. 61 


23 


13 


9 


77 


1 .60 


23 


14 


9 


95 


1. 41 


20 


15 


10 


11 


1 .60 


23 


16 


9 


68 


i-73 


25 


17 


9 


98 


1.50 


22 


18 


10 


44 


2.18 


3i 


19 


10 


11 


1.56 


22 


20 


10 


14 


2.09 


30 


21 


10 


79 


2-59 


37 



INDIVIDUAL DIFFERENCES 



43 



TABLE XV 

Accurates of Seventh and Eighth Grades 

The 343 cases are divided into ten groups on the basis of total amount 

done in forty-two minutes, going from lowest tenth to upper 

tenth. Below are given the averages for each group 



First 


{Lowest) 


Tenth — 35 Cases 


Second Tenth- 


—35 Cases 




Period 


Average 


A.D. F 


.E. 


Period Average 


A.D. 1 


'. E. 


I 


i-43 


1 .42 


07 


1 2.22 


1 .00 


14 


2 




86 


1-37 


06 


2 2.37 


.98 


14 


3 




77 


1. 19 


05 


3 2.20 


1 .09 


16 


4 




80 


.96 


04 


4 2.40 


1 .00 


14 


5 




49 


1 .01 


05 


5 2.55 


.62 


09 


6 




89 


•98 


04 


6 2.49 


•52 


07 


7 




67 


1.03 


06 


7 2.08 


.96 


13 


8 




52 


.92 


04 


8 2.69 


1.23 


17 


9 




80 


.88 


04 


9 2.40 


•85 


12 


10 




17 


•85 


04 


10 2.75 


•73 


10 


n 




83 


■83 


04 


11 2.43 


•93 


13 


12 




02 


.66 


03 


12 2.20 


•77 


11 


13 




54 


1 .04 


06 


13 2.45 


•94 


13 


14 




45 


•97 


04 


14 2.00 


•85 


12 


15 




40 


•97 


04 


15 2.45 


.92 


13 


16 




58 


.82 


04 


16 2.31 


115 


16 


17 




48 


1 .04 


06 


17 2.28 


1 .04 


15 


18 




22 


.84 


04 


18 2.34 


1 .02 


15 


19 




37 


•95 


04 


19 2.02 


•83 


12 


20 




3i 


•93 


04 


20 2.05 


.81 


12 


21 




14 


•7i 


03 


21 2.20 


1.08 


16 


Third Tenth — 34 Cases 




Fourth Tenth 


— 34 Cases 




Period 


Average 


A.D. I 


'. E. 


Period Average 


A.D. 1 


». E 


1 


3 -32 


1 .06 


18 


1 3-35 


1 .10 


16 


2 


2 


95 


.88 


12 


2 3 


36 


•78 


11 


3 


3 


26 


.80 


12 


3 3 


17 


1 .10 


16 


4 


3 


4i 


.82 


12 


4 3 


48 


.82 


12 


5 


3 


08 


•99 


H 


5 3 


44 


•79 


10 


6 


3 


05 


1 .06 


15 


6 3 


50 


.82 


12 


7 


3 


00 


•94 


13 


7 3 


23 


.84 


12 


8 


2 


89 


1 .09 


16 


8 3 


7i 


•92 


13 


9 


2 


74 


•9i 


13 


9 3 


23 


.87 


12 


10 


3 


17 


1.05 


16 


10 3 


53 


1.05 


15 


11 


3 


17 


1 .09 


16 


11 3 


68 


■94 


13 


12 


2 


54 


1 13 


16 


12 3 


17 


•95 


14 


13 


3 


14 


.88 


13 


13 3 


75 


1 .27 


18 



44 



MENTAL FATIGUE DURING CONTINUOUS EXERCISE 



TABLE XV (Continued) 
Accurates of Seventh and Eighth Grades 



Third Tenth — 34 Cases 
Period Average A.D. P.E. 



14 


2.69 


1.08 


16 


15 


2.74 


.89 


13 


16 


2.66 


1.05 


15 


17 


3.08 


1 .06 


15 


18 


2.83 


•84 


13 


19 


2.44 


1 .02 


15 


20 


2.71 


•93 


13 


21 


2-77 


1 .02 


15 




Fifth Tenth- 


— 34 Cases 




Period Average 


A.D. 1 


\E 


1 


4.09 


1. 10 


16 


2 


3-68 


1 .20 


15 


3 


3 56 


•93 


13 


4 


4-58 


.78 


11 


5 


3-59 


.96 


13 


6 


3-68 


■98 


14 


7 


3-77 


.90 


13 


8 


365 


.90 


13 


9 


3-91 


.78 


11 


10 


3.80 


•94 


13 


11 


4.00 


1. 11 


16 


12 


3-40 


1.08 


15 


13 


3-50 


•97 . 


14 


H 


3.80 


1. 19 


17 


15 


3-86 


1.06 


15 


16 


3.62 


•97 


14 


17 


3-8o 


.80 


12 


18 


3.65 


1.23 


18 


19 


3-ii 


.96 


14 


20 


3-59 


1. 41 ' 


20 


21 


3.20 


1. 41 


20 




Seventh Tenth 


— 34 Cases 




Perio 


d Average 


A.D. I 


\ E 


I 


4.66 


i-55 


22 


2 


4-58 


1 .29 


19 


3 


4.89 


1. 17 


17 


4 


5-09 


.96 


13 


5 


5.06 


.84 


12 



Fourth Tenth — 34 Cases 
Period Average A.D. P.E. 



14 


2 


95 


•95 


14 


15 


3 


38 


1 .01 


15 


16 


3 


53 


•99 


14 


17 


3 


59 


•99 


14 


18 


3 


33 


1 .09 


15 


19 


3 


11 


.76 


11 


20 


3 


14 


1.30 


19 


21 


3 


11 


1. 18 


16 




Sixth Tenth- 


— 35 Cases 




Period 


Average 


A.D. P.E 


1 


3-98 


1.49 


21 


2 


4 


44 


1 . 11 


16 


3 


4 


17 


1.03 


15 


4 


3 


89 


1 .01 


15 


5 


3 


67 


1.30 


19 


6 


4 


11 


1. 14 


16 


7 


4 


26 


1 .20 


17 


8 


4 


80 


1 .12 


16 


9 


4 


36 


•94 


14 


10 


4 


11 


1 .20 


17 


11 


4 


62 


•95 


H 


12 


4 


00 


.68 


10 


13 


4 


50 


1. 18 


16 


14 


3 


68 


1 .10 


16 


15 


4 


23 


1 .21 


17 


16 


4 


00 


1. 14 


16 


17 


4 


H 


•93 


13 


18 


4 


26 


1 .22 


18 


19 


4 


11 


■77 


11 


20 


4 


13 


1 .01 


15 


21 


4 


12 


1.30 


19 




Eighth Tenth 


— 34 Cases 




Period 


Average 


A.D. 1 


'. E 


I 


5-29 


1 .12 


17 


2 


4 


92 


.76 


11 


3 


5 


05 


1 .12 


16 


4 


5 


44 


1.05 


15 


5 


4 


83 


1. 19 


17 



■ UlM l WMMIim m »H* »MMWWW«MBq« 



BlinBSniHfMMH^HBnBfiSB^^HBragBBBBfl^aHHnBQEBHBIHBSBaOmaOB 



INDIVIDUAL DIFFERENCES 

TABLE XV {Continued) 
Accurates of Seventh and Eighth Grades 



45 



Seventh Tenth — 34 Cases 
Period Average A.D. P.E. 



6 


5 


03 




57 


08 


7 


4 


4i 


1 


04 


15 


8 


4 


77 




63 


09 


9 


4 


48 


1 


00 


14 


10 


4 


38 


1 


25 


17 


11 


4 


76 


1 


31 


19 


12 


4 


23 


1 


02 


15 


13 


4 


83 


1 


07 


15 


14 


4 


29 


1 


24 


17 


15 


4 


74 


1 


20 


17 


16 


4 


29 


1 


08 


16 


17 


4 


74 


1 


02 


15 


18 


4 


86 


1 


04 


15 


19 


4 


26 


1 


28 


17 


20 


4 


11 


1 


08 


16 


21 


4 


00 


1 


29 


18 




Ninth Tenth- 


— 34 Cases 




Period 


Average 


A.D. I 


\ E 


I 


5-95 


i-37 


19 


2 


5 


45 


1 .09 


16 


3 


5 


95 


1 .00 


14 


4 


5 


92 


■77 


11 


5 


5 


59 


1 .01 


15 


6 


5 


83 


•98 


13 


7 


5 


86 


.82 


12 


8 


6 


29 


1 .01 


15 


9 


5 


92 


•87 


13 


10 


5 


89 


1 .06 


15 


11 


5 


95 


1 . 12 


16 


12 


6 


08 


•99 


13 


13 


5 


83 


.98 


13 


H 


5 


80 


1 . 11 


16 


15 


5 


24 


1 .22 


17 


16 


5 


56 


1. 16 


17 


17 


6 


23 


■87 


13 


18 


5 


98 


1.09 


16 


19 


5 


83 


•95 


13 


20 


5 


55 


1.08 


16 


21 


5 


77 


1 


07 


15 





Eighth Tenth- 


— 34 Cases 




Period Average 


A.D. T 


.E 


6 


5-50 


1.08 


16 


7 


5 


17 




93 


13 


8 


5 


58 


1 


39 


19 


9 


5 


08 


1 


06 


15 


10 


5 


59 


1 


08 


16 


11 


5 


00 




94 


13 


12 


4 


7i 


1 


12 


16 


13 


5 


20 




90 


13 


14 


4 


95 


1 


12 


16 


15 


5 


35 


1 


4i 


16 


16 


5 


17 


1 


29 


18 


17 


5 


58 


1 


03 


15 


18 


4 


65 


1 


13 


16 


19 


4 


77 




92 


13 


20 


5 


11 


1 


18 


17 


21 


5 


00 


1 


11 


16 



Tenth Tenth — 34 Cases 
Period Average A.D. P.E. 



I 


7 


59 1 


43 


.20 


2 


7 


13 1 


25 


•17 


3 


7 


23 1 


5i 


.16 


4 


7 


80 1 


36 


.20 


5 


7 


14 1 


08 


.16 


6 


6 


89 1 


49 


.20 


7 


7 


08 1 


03 


•15 


8 


6 


92 1 


27 


•17 


9 


6 


98 1 


15 


.16 


10 


7 


42 1 


45 


.20 


11 


8 


02 1 


33 


.20 


12 


7 


35 1 


35 


.20 


13 


7 


95 1 


54 


.16 


14 


7 


32 1 


43 


.20 


15 


8 


32 1 


66 


.24 


16 


7 


62 1 


29 


•17 


17 


7 


38 1 


74 


■25 


18 


7 


32 1 


83 


.26 


19 


7 


17 1 


40 


.20 


20 


7 


17 1 


20 


.16 


21 


6 


83 1 


53 


.16 



46 MENTAL FATIGUE DURING CONTINUOUS EXERCISE 

TABLE XVI 

Third and Fourth Grades. — Attempts 
Sub- 
Groups I II III IV V VI VII VIII IX 

1 I 14 1-43 1.26 12% loss 1.37 1. 31 1.27 1. 00 

■95 
.92 

2 14 5 1.93 1.99 3% gain 1.92 1.88 2.01 1. 00 

• 97 

1 .04 

3 6 12 2.40 2.10 12% loss 2.40 2.41 2.19 1. 00 

1. 00 

•91 

4 3 1 2.84 2.72 4% loss 2.84 2.68 2.81 1. 00 

and .94 

7 -99 

5 2 12 3.22 3.06 5% loss 3.22 3. 11 3.13 1. 00 

.96 

•97 

6 4 12 3.59 3.45 4% loss 3.64 3.55 3.43 1. 00 

.96 
•94 

7 9 1 3-72 3-98 7% gain 3-75 3-94 4«3 100 

1.05 
1 .07 

8 8 12 4.22 4.16 1 % loss 424 4.40 4.22 1. 00 

1.037 
•99 

9 10 1 4.47 4.62 3% gain 4.65 4.81 4.84 1. 00 

1.034 
1.04 
10 9 1 5.65 6.54 16% gain 5.80 6.36 6.55 1. 00 

1 .09 
I 13 

Third and Fourth Grades — Accurates 

Sub- 
Groups I II III IV V VI VII VIII IX 

1 9 I .25 .21 16% loss .25 .28 .21 I. OO 

I. 12 
.84 

2 2 I .66 .55 17% loss .63 .64 .55 1. 00 
3 1 00 

.87 



INDIVIDUAL DIFFERENCES 47 

TABLE XVI (Continued) 

Third and Fourth Grades — Accurates 
Sub- 
Groups I II III IV V VI VII VIII IX 

3 2 i .97 .80 18% loss .98 .95 .80 1. 00 

.96 
.81 

4 11 12 1.34 .94 30% loss 1.36 1.22 1. 11 1. 00 

.89 
.81 

5 6 12 1.68 1.45 14% loss 1. 71 1. 61 1.49 1. 00 

•94 
.87 

6 6 14 2.01 1.66 17% loss 2.01 1.97 1.75 1. 00 

•98 

.87 

7 3 5 2.44 2.20 10% IOSS 2.51 2.21 2.29 I. OO 

4 .88 

•91 

8 3 12 2.81 2.46 12% loss 2.85 2.86 2.63 1. 00 

1.003 
.92 

9 8 1 3.21 3.25 i%gain 3.32 3.37 3.27 1.00 

1. 01 

.98 

10 9 1 4.37 4.21 4% loss 4.38 4.59 4.30 1.00 

1.04 

.98 

TABLE XVII 

Seventh and Eighth Grades — Attempts 
Sub- 
Groups I II III IV V VI VII VIII IX 

1 1 12 3.50 3.53 5% loss 3.44 3.14 3.21 1. 00 

•9i 
•93 

2 5 19 4-50 4-30 5% loss 4.38 4.07 4.32 1.00 

•93 
.98 

3 13 21 4.82 4.29 11% loss 4.70 4.69 4.66 1. 00 

•99 
•99 

4 13 18 4.90 4.87 i%loss 4.97 5.13 4.93 1. 00 

1.03 

•99 



48 MENTAL FATIGUE DURING CONTINUOUS EXERCISE 

TABLE XVII (Continued) 

Seventh and Eighth Grades — Attempts 
Sub- 
Groups I II III IV V VI VII VIII IX 

5 15 19 5-34 4-99 7% loss 5.32 5.62 5.45 1.00 

1.05 
1.02 

6 20 5 5.87 6.13 4% gain 5.80 5.95 6.07 1.00 

1 .02 
1 .04 

7 15 19 6.25 6.10 2% loss 6.21 6.23 6.42 1. 00 

I .00 

1.03 

8 15 14 6.91 6.86 i%loss 6.74 6.73 7.01 1. 00 

■99 
1 .04 

9 15 17 7.42 7.78 5% gain 7.37 7.53 7.53 1. 00 

1.02 

1 .02 

10 21 2 8.92 10.35 16% gain 9.10 9.38 10.18 1.04 

1.03 

1. 12 

Seventh and Eighth Grades — Accurates 
Sub- 
Groups I II III IV V VI VII VIII IX 

1 10 12 1.69 1.27 25% loss 1.70 1.62 1.36 1. 00 

•95 
.80 

2 10 14 2.26 2.09 8% loss 2.33 2.42 2.23 1. 00 

1.08 

•95 

3 4 19 3.18 2.64 17% loss 3.15 2.91 2.75 1. 00 

.92 
.87 

4 13 14 3.29 3.12 5% loss 3.36 3.43 3.31 1. 00 



4 19 3-78 3-30 13% loss 3.85 3.23 3.55 1. 00 

.84 

.92 

8 5 4.20 4.12 2% loss 4.07 4.29 4.14 1. 00 

1.05 
1. 01 

4 21 4.7O 4-12 12% loss 4.82 4.63 4.42 1. 00 

•93 
•91 



INDIVIDUAL DIFFERENCES 49 

TABLE XVII {Continued) 

Seventh and Eighth Grades — Accurates 
Sub- 

Groups I II III IV V VI VII VIII IX 

8 10 18 5.09 4.96 3% loss 5.17 5.16 5.09 1. 00 

•99 

.98 

982 5.78 5.72 1 % loss 5-79 5-97 5-88 1.00 

1.03 

1. 01 
10 15 21 7.32 7. 11 3%loss 7.27 7.42 7.42 1. 00 

1 .02 
1 .02 

EXPLANATION OF TABLES NOS. XVI AND XVII 

In these tables we have under 

I. The maximum period for each curve. 

II. The minimum period for each curve. 

III. Average columns for first three periods. 

IV. Average columns for last three periods. 

V. Per cent, of gain or loss when III and IV are compared with III as a basis. 
VI. Average of first third of curve. 
VII. Average of second third of curve. 
VIII. Average of last third of curve. 
IX. Relative value of VI, VII, and VIII, using VI as a basis. 
The figures under V show that the group fatigued or did not fatigue — accord- 
ing as there was loss or gain. IX gives an idea of the general form of the curve. 

To begin with the facts as summarized in Table XVI. The 
location of the maximum (Column I) is certainly later with the 
better workers, when attempts are considered, in either the Third 
and Fourth or the Seventh and Eighth grades; the minimum, on 
the other hand, tends to come earlier with the better groups than 
with the poorer. In the case of accurates, no clear relation appears 
between the location of the maximum or minimum and the total 
accomplishment. 

Column V shows pretty clearly that the losses tend to be smaller 
towards the bottom of the column, which means that the better 
workers fatigued less than the poorer workers. In the case of 
attempts, the loss actually gives way to a gain, while in the case of 
accurates, the best workers lose very little at the end as compared 
with the beginning. Column IX, attentively considered, will show 
the same thing. 



50 



MENTAL FATIGUE DURING CONTINUOUS EXERCISE 



But, undoubtedly, the best presentation of the results is afforded 
by the curves. 1 The curves for attempts, in both the younger and 
the older group, show a clear general rise in the case of the upper 
tenth, indicating that the best workers increased their speed during 
the experiment; while the curve for the lowest tenth shows the 



c 4 

a 

"o 

u 



I - 



C 




=4= 



=£= 



Periods 



14 



24 6 8 10 12 

Fig. 9. Attempts — Third and Fourth Grades 

EXPLANATION OF FIGURES 9-12 
The points on these curves are for the average performances for every four 
minutes, the data being handled thus so as to smooth out the curves. 

opposite course. The curves for the intervening tenths are rather 
confusing, but apparently have no definite tendency to deviate 
much from the horizontal — which would indicate that, on the whole, 
the medium workers neither increased nor decreased their speed. 

1 See Figures 5, 6, 7, and 8 on pages 31, 32, 33 and 34 



INDIVIDUAL DIFFERENCES 51 

The curves for accurates fail to reveal to the eye any clear dif- 
ference between the sub-groups. 

Evidently we have made too many sub-groups in dividing into 
tenths. While highest and lowest tenths should evidently be kept 
separate, as their curves stand so definitely apart from the rest, 
the second and third tenths may very well be combined, and like- 
wise the eighth and ninth, leaving the four middle tenths to com- 






u 



C 
ft 



I III | i w*m I ty i Im i I. I inn ■ ■# 



Periods 2 4 6 8 10 12 14 

Fig. 10. Accurates — Third and Fourth Grades 

bine into one central group. The resulting division into five 
unequal parts gives approximately equal spaces between the aver- 
ages of the adjacent groups, as should be the case according to the 
theory of distribution, and as appears in fact to be the case in the 
following curves constructed as above indicated. In order further 
to eliminate irrelevant fluctuations, the points on the curves indi- 
cate the averages of two adjacent periods of two minutes. The 
Tables, XVIII to XXI, give the averages for each period. Group A, 
in these tables, consists of the lowest tenth, Group B of the second 



52 



MENTAL FATIGUE DURING CONTINUOUS EXERCISE 



and third tenths, Group C of the fourth to seventh tenths, Group 
D of the eighth and ninth, and Group E of the uppermost tenth. 



ii I- 



a 6 




5 -3? 



. 




i i i i \ I 1 I i i I t 



x 



j i i i 



™4- 



Periods 24 6 8 10 12 14 16 18 20 21 

Fig. 11. Attempts — Seventh and Eighth Grades 

The curves, thus reduced to their lowest terms, indicate pretty 
clearly that there is a relation in attempts between speed of work 
and liability to fatigue. The most rapid workers increase their 
speed as time goes by, while the slowest workers fall off, the middle 
groups remaining, on the average, almost perfectly steady for the 
time here considered. In accurate work, the general tendency of 
the whole group was shown in the last chapter to be slightly down- 
ward towards the end. But the decline comes later with the upper 



m 



INDIVIDUAL DIFFERENCES 53 

group, and is somewhat less pronounced than in the lowermost 
group, at least when the decline is considered in relation to the 
height of the curve above the base line. This is brought out by 
another way of examining the results. 



8 


£ 


x ^ -^ ^»^ 


7 






6 


D 


^r*~ — ~ ^ x 


03 B 

c 5 
S 

3 
"3 

U 4 


C 


„^— ^^ 


3 


j5 


^^-- > '" 


2 


A 




I 







Periods 246 8 10 12 14 16 

Fig. 12. Accurates — Seventh and Eighth Grades 

As heretofore, the first three periods were compared with the 
last three periods. The results are given below : 

Third and Fourth Grades 
Attempts Accurates 

Group A, 12 per cent, loss Group A, 16 per cent, loss 

Group B, 5 per cent, loss Group B, 18 per cent, loss 

Group C, 1 per cent, loss Group C, 18 per cent, loss 

Group D, 1 per cent, gain Group D, 6 per cent, loss 

Group E, 16 per cent, gain Group E, 4 per cent, loss 

Seventh and Eighth Grades 

Attempts Accurates 

Group A, 5 per cent, loss Group A, 25 per cent, loss 

Group B, 8 per cent, loss Group B, 12 per cent, loss 

Group C, 1 per cent, loss Group C, 8 per cent, loss 

Group D, 2 per cent, gain Group D, 2 per cent, loss 

Group E, 16 per cent, gain Group E, 3 per cent, loss 



54 



MENTAL FATIGUE DURING CONTINUOUS EXERCISE 



In the case of attempts, the relation between total speed and 
fatigue comes out in this tabulation as clearly as before. The loss 
shown by the slowest groups gives way to a gain with the quickest 
workers. In the case of accurates, the change is certainly less clear, 
and there is no passing over to a gain; yet it may fairly be said 
that the better groups show a smaller loss than the poorer. 

The facts of Column IX in Tables XVI and XVII are taken for 
the Groups A, B, C, D, and E of the previous tabulation. The 
facts for the lowest tenth are the facts for Group A, the second and 
third tenth are those for Group B, etc. 









Third and Fourth Grades 








A ttempts 


i 


2 


3 


Accurates 


1 


2 


3 


Group 








Group 








A 


I .00 


•95 


.92 


A 


1. 00 


1 . 12 


84 


B 


i .00 


•985 


•975 


B 


1 .00 


.98 


84 


C 


1 .00 


•99 


•99 


C 


1 .00 


.92 


87 


D 


1 .00 


1-035 


1. 015 


D 


1 .00 


1 .01 


95 


E 


1 .00 


1 .09 


1 13 


E 


1 .00 


1.04 


98 






Seventh and Eighth Grades 








Attempts 


1 


2 


3 


Accurates 


1 


2 


3 


Group 








Group 








A 


1 .00 


• 91 


•93 


A 


1 .00 


■95 


80 


B 


1 .00 


.96 


•985 


B 


1 .00 


1 .00 


91 


C 


1 .00 


1 .028 


1 .02 


C 


1 .00 


.96 


955 


D 


1 .00 


1.005 


1.03 


D 


1. 00 


1 .01 1 


005 


E 


1 .00 


1.03 


1 . 12 


E 


1 .00 


1 .02 1 


02 



In the case of attempts, the relation between total speed and 
liability to fatigue is about as clear in this present tabulation as it 
was in the previous one. The quickest workers gain and the 
poorest workers lose. In the case of accuracy the change is clearer, 
for in the younger classes the better workers show a smaller loss 
than the poorer ones and in the older classes the best workers 
show a small gain. Consequently this way of examining the 
results supports the conclusion that on the whole the slower work- 
ers fatigue more quickly than the more rapid workers. 

This, then, is put forward as one of the chief results of the experi- 
ment: that, on the whole, the slower workers fatigue more quickly 
than the more rapid workers. 



imiiiiiimiimn.iB.il 



INDIVIDUAL DIFFERENCES 

TABLE XVIII 

Attempts, Third and Fourth Grades 



55 





Group I 


Groups 


Groups I V, 


Groups 


Group . 






II, III 


V, VI, VII, 


VIII, IX 






A 


B 


C 


D 


E 


I 


1-52 


2.13 


3-04 


4-25 


5-16 


2 


i 


5o 


2.13 


3 


46 


4 


31 


5-75 


3 


i 


27 


2.23 


3 


52 


4 


4i 


6.05 


4 


i 


19 


2. 12 


3 


43 


4 


75 


6.25 


5 


i 


44 


2.08 


3 


17 


4 


39 


5-78 


6 


i 


36 


2. 17 


3 


43 


4 


65 


5-92 


7 


i 


22 ' 


2. 17 


3 


21 


4 


47 


6.61 


8 


i 


33 


2.15 


3 


34 


4 


82 


6.58 


9 


i 


22 


2.19 


3 


34 


4 


72 


6.92 


IO 


i 


36 


2. 17 


3 


44 


4 


82 


6-75 


ii 


i 


22 


2.21 


3 


66 


4 


66 


6.36 


12 


i 


33 


195 


3 


19 


4 


29 


6.52 


13 


i 


38 


2. 11 


3 


43 


4 


48 


6.41 


14 


i 


08 


2. 12 


3 


28 


4 


39 


6.70 



TABLE XIX 

Accurates, Third and Fourth Grades 





Group I 


Groups 


Groups IV, 


Groups 


Group 






II, III 


V, VI, VII 


VIII, IX 






A 


B 


C 


D 


E 


I 


•13 


•5i 


1 65 


2.61 


3.84 


2 


•35 


1 .00 


1 


94 


3.18 


4 


50 


3 


.27 


■97 


2 


02 


3-24 


4 


78 


4 


.24 




76 


1 


99 


3-30 


4 


41 


5 


•29 




86 


1 


64 


3-«3 


4 


19 


6 


•32 




81 


1 


98 


3-05 


4 


67 


7 


.21 




77* 


1 


68 


2.90 


4 


47 


8 


.16 




86 


1 


78 


3-45 


4 


73 


9 


.40 




73 


1 


69 


314 


4 


89 


10 


.21 




77 


1 


81 


3.00 


4 


55 


11 


.21 




60 


1 


80 


3.20 


4 


33 


12 


.21 




74 


1 


40 


2.68 


4 


25 


13 


•24 




63 


1 


74 


3 09 


4 


08 


14 


.18 




65 


1 


55 


2.78 


4 


30 



56 MENTAL FATIGUE DURING CONTINUOUS EXERCISE 

TABLE XX 

Attempts — Seventh and Eighth Grades 





Group I 


Groups 


Groups I V, 


Groups 


Group 






II, III 


V, VI, VII 


VIII, IX 






A 


B 


C 


D 


E 


I 


3-7i 


4-77 


5.66 


7 56 


9.29 


2 


3-42 


4 


79 


5 


47 


6-75 


8 


61 


3 


3-37 


4 


43 


5 


64 


7.18 


8 


86 


4 


3-66 


4 


4i 


5 


72 


7.22 


9 


44 


5 


3-17 


4 


38 


5 


24 


6.77 


8 


93 


6 


3-55 


4 


44 


5 


75 


7-45 


8 


89 


7 


3-17 


4 


08 


5 


63 


6-93 


8 


98 


8 


3.08 


4 


39 


5 


68 


7.40 


8 


95 


9 


3.20 


4 


4i 


5 


55 


6.98 


8 


83 


10 


3 40 


4 


65 


5 


86 


7.22 


9 


38 


ii 


3-15 


4 


50 


5 


74 


7.28 


9 


77 


12 


2.83 


4 


11 


5 


60 


6.92 


9 


52 


13 


3.22 


4 


59 


5 


93 


7.18 


9 


77 


14 


3 09 


3 


99 


5 


93 


6.92 


9 


95 


15 


2.87 


4 


48 


6 


25 


7.91 


10 


1 1 


16 


3 25 


4 


52 


5 


81 


6.98 


9 


68 


17 


3-31 


4 


68 


5 


85 


6.94 


9 


98 


18 


3.06 


4 


38 


5 


54 


703 


10 


44 


19 


3-57 


4 


09 


5 


11 


6-95 


10 


11 


20 


3-57 


4 


57 


5 


73 


7.48 


10 


14 


21 


2.86 


4 


22 


5 


70 


7-53 


10 


79 



INDIVIDUAL DIFFERENCES 



57 



TABLE XXI 
Accurates, Seventh and Eighth Grades 



Group I 


Groups 


Groups IV, 


Groups 


Group . 






II, III 


V, VI, VII 


VIII, IX 




A 


B 


C 


D 


E 


I i 


43 


2.72 


4.02 


5 62 


7-59 


2 I 


86 


2.66 


4 


01 


5 


19 


7-13 


3 i 


77 


2-73 


3 


89 


5 


50 


7-23 


4 i 


8o 


2.90 


4 


26 


5 


68 


7.80 


5 i 


49 


2.82 


4 


19 


5 


21 


7.14 


6 i 


89 


2.77 


4 


08 


5 


66 


6.89 


7 i 


67 


2-54 


3 


92 


5 


56 


7.08 


8 I 


52 


2.79 


4 


24 


5 


94 


6.92 


9 i 


80 


2-57 


3 


99 


5 


50 


6.98 


10 2 


17 


2.96 


3 


95 


5 


74 


7.42 


II I 


83 


2.80 


4 


26 


5 


47 


8.02 


12 I 


02 


2-37 


3 


70 


5 


39 


7-35 


13 I 


54 


2.79 


4 


14 


5 


52 


7-95 


14 I 


45 


2-34 


3 


68 


5 


37 


7-32 


15 i 


40 


2-59 


4 


05 


5 


79 


8.32 


16 i 


58 


2.48 


3 


85 


5 


36 


7.62 


17 i 


48 


2.68 


4 


07 


5 


90 


7-38 


18 I 


22 


2.58 


4 


02 


5 


32 


7-32 


19 i 


37 


2.23 


3 


65 


5 


30 


7-32 


20 I 


3i 


2.38 


3 


77 


5 


33 


7.17 


21 I 


14 


2.49 


3 


58 


5 


39 


6.83 



CHAPTER IV 
VARIABILITY OF THE INDIVIDUAL 

Dependence of Variability upon Central Tendency 

Everyone feels that variability is bound to increase as the mea- 
sure of performance increases. There is evidently some dependence 
of variability upon the absolute measure of performance, such 
that the greater the absolute measure of performance the greater 
the variability. 

Pearson has accepted the common-sense idea regarding this 
dependence, i.e., that variability is normally or typically propor- 
tional to the absolute measure of performance. Fullerton and 
Cattell, and Thorndike, following the rule governing the variable 
error in the theory of measurement, have held that the variability 
normally increases as the square root of the absolute measure of 
performance, though probably with modifications in different kinds 
of performance. 

Our data afford the opportunity of examining the variability of 
each individual from one period to another of the fourteen or 
twenty-one two-minute periods of the test, and then comparing the 
variability of individuals with smaller and greater total (or average) 
performance. This would be little to the purpose if a pronounced 
practice or fatigue effect occurred within the limits of the work; 
but, as these effects have been shown to be rather slight, the varia- 
bility that appears in the individual's performance can be accepted 
as, in the main, simply the ordinary variability of performance. 



UmMMNW 



*^ 



VARIABILITY OF THE INDIVIDUAL 59 

TABLE XXII 

Accurates of Third and Fourth Grades, showing average performance and 
variability of each individual for the twenty-eight minutes 



"otal Average /. 


. D. 


C. T.ofA.D.'s 






















.07 


•13 






.07 


•13 






.07 


•13 






07 


• 13 






07 


13 


■13 


2 


14 


25 




2 


14 


25 




2 


14 


25 




2 


14 


25 




2 


14 


25 


■25 


3 


21 


34 




3 


21 


34 




3 


21 


34 




3 


21 


34 




3 


21 


34 


•34 


4 


29 


42 




4 


29 


42 




4 


29 


42 




4 


29 


46 




4 


29 


46 




4 


29 


46 


•44 


5 


36 


73 




5 


36 


73 




5 


36 


66 




5 


36 


66 




5 


36 


66 




5 


36 


66 




5 


36 


66 


.68 


6 


43 


63 




6 


43 


57 




6 


43 


57 




6 


43 


63 




6 


43 


57 




6 


43 


50 




6 


43 


63 




6 


43 


57 


•58 


7 


50 


64 




7 


50 


61 




7 


50 


61 





6o 



MENTAL FATIGUE DURING CONTINUOUS EXERCISE 



TABLE XXII (Continued) 



"otal Average A 


. D. 


C. T.ofA.D.'s 


7 


50 


54 




7 


50 


54 




7 


50 


61 




7 


50 


61 




7 


50 


74 




7 


50 


54 


.60 


8 


57 


60 




8 


57 


52 




8 


57 


67 




8 


57 


60 




8 


57 


60 




8 


57 


60 


.60 


9 


64 


57 




9 


64 


73 




9 


64 


64 




9 


64 


42 




9 


64 


53 




9 


64 


53 




9 


64 


65 




9 


64 


53 


.58 


IO 


7i 


52 




IO 


71 


46 




IO 


7i 


63 




IO 


71 


75 




IO 


7i 


82 




IO 


7i 


75 




IO 


7i 


75 




IO 


7i 


68 




IO 


7i 


72 




IO 


71 1 


04 




IO 


7i 


72 




IO 


7i 


72 




IO 


71 


81 


•72 


II 


•79 


.67 




II 


• 79 


.69 




II 


•79 


•97 




II 


•79 


.81 




II 


• 79 


•9i 


.81 


12 


.86 


.48 




12 


.86 


•74 




12 


.86 


•34 




12 


.86 


.63 




12 


.86 


•74 




12 


.86 


.61 








VARIABILITY OF THE INDIVIDUAL 



61 





TABLE XXII (C 


ontinn 


ed) 




Total 


.<4z>erage ^ 


.D. 


C. T.ofA.D. 


's 


12 


.86 


52 






12 




86 


52 






12 




86 i 


52 






12 




86 


73 






12 




86 


73 


.69 




13 




93 


80 






13 




93 


53 






13 




93 


68 






13 




93 


70 






13 




93 


80 






13 




93 


70 






13 




93 


57 






13 




93 


68 






13 




93 


52 






13 




93 I 


05 






13 




93 


70 


.70 




14 


I 


oo 


44 






14 


i 


00 


73 






14 


i 


oo 


29 






H 


i 


oo 


73 






14 


i 


oo 


58 






H 


I 


00 


87 






14 


I 


00 


44 






14 


i 


oo 


73 






14 


i 


oo 


86 






14 


I 


00 


58 






14 


i 


oo 


57 






14 


i 


oo 


71 


•63 




15 


i 


07 


92 






15 


i 


07 


63 






15 


I 


07 


34 






15 


i 


07 


53 






15 


i 


07 


53 






15 


i 


07 


66 






15 


i 


07 


73 






15 


i 


07 


66 






15 


i 


07 


63 






15 


i 


07 


63 






15 


i 


07 


80 


.64 




16 


i 


14 


62 






16 


I 


14 


64 






16 


i 


14 


60 






16 


i 


14 


75 


•65 




17 


i 


21 


56 


•56 





62 



MENTAL FATIGUE DURING CONTINUOUS EXERCISE 



Total 



TABLE XXII {Continued) 

Average A.D. C. T. of A. D.'s. 



18 I 


29 


8 1 


18 I 


29 


61 


18 I 


29 


72 


18 i 


29 


64 


18 I 


29 


61 


18 I 


29 


75 


18 i 


29 


94 


19 1 


36 


73 


19 1 


36 


57 


19 I 


36 


69 


19 1 


36 


98 


19 1 


36 1 


II 


19 1 


36 


73 


19 1 


36 


54 


19 1 


36 


74 


19 I 


36 


■S3 


19 1 


36 


78 


20 1 


43 


64 


20 1 


43 


69 


20 1 


43 


72 


20 1 


43 


77 


20 1 


43 


63 


20 1 


43 


63 


20 1 


43 


7-' 


20 1 


43 


63 


21 1 


50 


86 


21 1 


50 


7i 


21 1 


50 


57 


21 1 


50 


50 


21 1 


50 1 


00 


21 1 


50 


78 


21 1 


50 


64 


22 1 


57 


55 


22 1 


57 


55 


22 1 


57 


83 


22 1 


57 


57 


22 1 


57 


91 


22 1 


57 


57 


22 1 


57 


97 


23 1 


64 


82 


23 1 


64 


69 


23 1 


64 1 


21 


23 1 


64 


59 


23 1 


64 


44 



.72 



■77 



.68 



.72 



.70 



II ■ 



VARIABILITY OF THE INDIVIDUAL 



TABLE XXII (Continued) 



63 



Total Average 


A.D. 


C. T.ofA.D.'s 


23 1 


64 


82 




23 1 


64 


1.08 


.80 


24 1 


7i 


•75 




24 1 


7i 


•75 




24 1 


7i 


•75 




24 1 


7i 


•75 




24 1 


7i 


1 .02 




24 1 


7i 


.72 




24 1 


7i 


•65 




24 1 


7i 


•55 




24 1 


71 


.89 




24 1 


71 


1 .02 




24 1 


7i 


•75 




24 1 


7i 


.90 


•79 


25 1 


79 


1.09 




25 1 


79 


.72 




25 1 


79 


1.07 




25 . 1 


79 


1 .09 




25 ' 1 


79 


1.50 




25 1 


79 


.72 




25 1 


79 


•72 




25 r 


79 


•93 




25 1 


79 


•44 


.92 


26 1 


86 


• 87 




26 1 


86 


■63 




26 1 


86 


.87 




26 1 


86 


.89 




26 1 


86 


1.28 




26 1 


86 


.87 




26 1 


86 


.87 




26 1 


86 


1 .00 


•9i 


27 1 


93 


.66 




27 1 


93 


•93 




27 1 


93 


.66 




27 1 


93 


■95 




27 1 


93 


.66 


■77 


28 2 


00 


.84 




28 2 


00 


■58 




28 2 


00 


.70 




28 2 


00 


.70 




28 2 


00 


.70 




28 2 


00 


1.06 




28 2 


00 


.70 




j»9 2 


07 


•93 





64 MENTAL FATIGUE DURING CONTINUOUS EXERCISE 

TABLE XXII (Continued) 



Total 


Average 


A.D. 


C. T.ofA.D.'s. 


29 


2.07 


.66 




29 


2.07 


1.08 




29 


2.07 


• 79 




29 


2.07 


.66 


.82 


30 


2.14 


.86 




30 


2.14 


.62 




30 


2.14 


.98 




30 


2.14 


.86 




30 


2. 14 


.62 




30 


2.14 


.86 


.80 


31 


2.21 


.80 




3i 


2.21 


•73 




31 


2.21 


.84 




3i 


2.21 


1 .04 




3i 


2.21 


•95 




3i 


2.21 


■49 


.81 


32 


2.28 


1.03 




32 


2.28 


•59 




32 


2.28 


•93 




32 


2.28 


•50 




32 


2.28 


•75 




32 


2.28 


1.23 


.84 


33 


2.36 


1. 16 




33 


2.36 


• 78 




33 


2.36 


.68 




33 


2.36 


.78 




33 


2.36 


•83 




33 


2.36 


.68 




33 


2.36 


•78 • 




33 


2.36 


.83 




33 


2.36 


.68 




33 


2.36 


•87 




33 


2.36 


•78 




33 


2.36 


.68 


.80 


34 


2-43 


1.04 




34 


2-43 


•85 




34 


2-43 


•78 




34 


2-43 


.90 


.89 


35 


2.50 


•93 




35 


2.50 


•85 




35 


2.50 


1 13 




35 


2.50 


•63 




35 


2.50 


1. 00 




35 


2.50 


1.05 


•94 



MMHUMI 



VARIABILITY OF THE INDIVIDUAL 65 

TABLE XXII {Continued) 



Total 


Average 


A.D. 


C. T.ofA.D.'s 


36 


2.58 


.70 




36 


2.58 


.90 




36 


2.58 


1. 19 




36 


2.58 


1.29 




36 


2.58 


.70 


•95 


37 


2.64 


1.24 




37 


2.64 


1 .06 




37 


2.64 


1. 16 




37 


2.64 


.69 




37 


2.64 


.98 




37 


2.64 


1. 00 




37 


2.64 


.82 


.96 


37 


2.64 


.69 




38 


2.71 


.76 




38 


2.71 


i-43 




38 


2.71 


1. 17 




38 


2.71 


•95 




38 


2.71 


•79 


1.02 


39 


2-79 


.70 




39 


2.79 


•73 




39 


2.79 


•84 




39 


2-79 


.81 




39 


2-79 


1.26 


.87 


40 


2.86 


.60 




40 


2.86 


.92 




40 


2.86 


•74 




40 


2.86 


•78 


.76 


4i 


2-93 


.82 




41 


2-93 


.64 




41 


2-93 


•94 




41 


2-93 


1.20 




41 


2-93 


•94 


•91 


42 


300 


1 .20 




42 


3.00 


•94 




42 


3.00 


•57 




42 


3.00 


.66 




42 


3.00 


•54 




42 


3.00 


.66 




42 


3.00 


.81 




42 


3.00 


1.08 


■73 


43 


307 


1. 14 




43 


3 07 


.92 




43 


307 


■77 




43 


307 


.80 





66 



MENTAL FATIGUE DURING CONTINUOUS EXERCISE 



TABLE XXII {Continued) 



Total 


Average A 


.D. 


C. T.ofA.D.'s 


43 


3-07 


52 




43 


3 


07 


37 


•75 


44 


3 


14 


66 




44 


3 


14 1 


16 




44 


3 


14 1 


16 


•99 


45 


3 


21 


83 




45 


3 


21 1 


06 




45 


3 


21 


93 




45 


3 


21 1 


09 


.98 


46 


3 


28 


98 




46 


3 


28 


79 




46 


3 


28 


89 




46 


3 


28 


98 




4.6 


3 


28 


89 


•9i 


47 


3 


36 


9i 




47 


3 


36 


74 




47 


3 


36 


81 




47 


3 


36 1 


01 




47 


3 


36 


91 




47 


3 


36 


67 


.84 


48 


3 


43 1 


20 




48 


3 


43 


93 




48 


3 


43 


99 




48 


3 


43 1 


13 




48 


3 


43 


99 




48 


3 


43 1 


13 




48 


3 


43 


99 


1.05 


49 


3 


50 


63 




49 


3 


50 


84 




49 


3 


50 


77 




49 


3 


50 


84 


■77 


50 


3 


57 


7i 


■71 


51 


3 


64 


76 




51 


3 


64 


61 




5i 


3 


64 


.80 


.72 


52 


3 


71 1 


04 




52 


3 


7i 


74 


.89 


54 


3 


86 1 


00 




54 


3 


86 1 


15 




54 


3 


86 


73 


.96 


55 


3 


93 1 


06 




55 


3 


93 


79 




55 


3 


93 


94 




55 


3 


93 


94 


•94 



yvihiiiiuiiuiih 



VARIABILITY OF THE INDIVIDUAL 



67 





TABLE XXII 


{Continued) 




Total 


Average 


A.D. 


C. 


T.ofA.D.'s 


56 


4.00 


•56 




•56 


57 


4 


07 


•77 






57 


4 


07 


•77 




•77 


58 


4 


14 


•75 






58 


4 


14 


1. 41 






58 


4 


H 


1. 16 




1. n 


59 


4 


21 


•93 






59 


4 


21 


1. 18 




1.06 


60 


4 


28 


•47 






60 


4 


28 


.68 




•57 


61 


4 


36 


1 .09 




1 .09 


62 


4 


43 


I-5I 






62 


4 


43 


1 .02 




1 .26 


64 


4 


57 


.96 






64 


4 


57 


.96 




.96 


65 


4 


64 


•74 




•74 


66 


4 


7i 


1 .04 




1.04 


68 


4 


86 


•87 




•87 


70 


5 


00 


.70 




.70 


7i 


5 


07 


.66 




.66 


72 


5 


14 


.87 




.87 


73 


5 


21 


•83 




•83 


76 


5 


43 


1.03 




1.03 


85 


6 


07 


1 .21 




1 .21 


no 


7 


85 


I .02 




1.02 



TABLE XXIII 

Showing the Data for Third and Fourth Grades, Accurates with 
C. T.'s and Average A. D.'s Combined into Twelve Groups 





C. T. 


A 


.D 


.07 to .43 


40 




50 to 


86 


67 




93 to 1 


29 


65 


1 


36 to 1 


7i 


75 


I 


79 to 2 


14 


13 


2 


21 to 2 


58 


87 


2 


67 to 3 


00 


88 


3 


07 to 3 


43 


92 


3 


50 to 3 


86 


81 


3 


93 to 4 


28 


84 


4 


36 to 5 


21 


90 


5 


43 to 7 


85 1 


09 



The twelve groups given here were obtained by combining the data of Table 
XXII so that as nearly as possible the twelve groups would proceed by steps of .36. 
The data would not submit to this treatment in the last two groups of the twelve. 



68 



MENTAL FATIGUE DURING CONTINUOUS EXERCISE 



TABLE XXIV 

Attempts, Third and Fourth Grades, Showing Average Performance 

and Average Variability of Certain Groups of Individuals for 

the Twenty-eight Minutes. Eighty-five Groups 



Number of Columns 


Number of Columns 


Number of Columns 


C. T. Average 


C. T. Average 


C. T. Average 


of A.D. 


of A.D. 


of A.D. 


.28 


55 


2.36 


62 


4.07 


49 


•43 


49 


2-43 


52 


4 


14 


81 


.64 


55 


2.50 


67 


4 


21 


60 


.78 


34 


2-57 


53 


4 


28 


70 


.86 


24 


2.64 


4i 


4 


35 


79 


1. 00 


10 


2.71 


67 


4 


43 


67 


1.07 


13 


2.78 


54 


4 


50 


68 


1. 14 


29 


2.86 


59 


4 


57 


62 


1. 21 


46 


2-93 


4i 


4 


64 


71 


1.28 


4i 


3.00 


42 


4 


7i 


89 


1-35 


60 


307 


68 


4 


78 1 


18 


1-43 


56 


3-14 


53 


4 


85 


55 


1.50 


58 


3.21 


49 


4 


93 


42 


i-57 


57 


3-28 


67 


5 


00 


33 


1.64 


47 


3-35 


55 


5 


07 


95 


1. 71 


58 


3-43 


66 


5 


14 1 


08 


1.78 


54 


3-50 


66 


5 


21 


42 


1.83 


47 


3-57 


64 


5 


28 


60 


i-93 


37 


364 


56 


5 


36 


62 


2.00 


46 


3-71 


71 


5 


43 


65 


2.07 


37 


3-78 


60 


5 


50 


64 


2.21 


55 


3-92 


49 


5 


64 


53 


2.28 


56 


4.00 


23 


5 
5 
5 
6 
6 
6 
6 
6 
6 
7 
7 
8 

9 
13 


78 
85 
93 
00 
07 
28 

43 

50 2 

93 
00 

43 
7i 
79 < 

6 4 ; 


58 
51 
82 

57 
67 
79 

72 

H 
53 
43 
92 

78 
J.21 

5.72 



wmaoomimiMiiimii 



VARIABILITY OF THE INDIVIDUAL 69 

TABLE XXV 

Showing Data for the Foregoing Table Combined into Twelve Groups 

Average 
of A. D. 
.46 
•45 
•58 
•51 
■59 
63 
■55 
73 
69 
67 
81 
4i 

In this table we proceed as nearly by steps of .36 as possible. The first group 
and last four groups could not well be made to fulfill this condition. But as this 
does not affect the mathematical significance of the results, it matters little. 





C. T 




.28 to 


1. 71 


I 


78 to 


2. 14 


2 


25 to 


2-57 


2 


64 to 


3.00 


3 


07 to 


3-43 


3 


50 to 


3-86 


3 


92 to 


4.28 


4 


35 to 


4-71 


4 


78 to 


5-28 


5 


36 to 


5 -7o 


5 


78 to 


6-93 


7 


00 to 


13.64 



TABLE XXVI 

Accuracy, Seventh and Eighth Grades, Showing Average Performance 

and Average Variability of Certain Groups of Individuals for 

the Forty-two Minutes of Working. There are 122 Groups 



Number of Columns 



Number of Columns 



Number of Columns 



c 


'. T. Am 


'.rage 


C. T. 


Average 


C 


T. 


Average 


ofA.D. 




ofA.D. 




ofA.D. 


•43 


53 


2.38 


1 . 10 


3-57 


1.05 




48 


59 


2-43 


1 .21 


3 


62 


1 


00 




62 


65 


2.48 


1.07 


3 


67 




90 




7i 


82 


2.52 


•83 


3 


7i 


1 


24 




76 


58 


2-57 


1.30 


3 


76 


1 


08 




90 


61 


2.62 


1 .01 


3 


81 


1 


15 


1 


04 


93 


2.67 


1.04 


3 


86 


1 


23 


1 


29 


92 


2.71 


■99 


3 


90 




65 


1 


33 


51 


2.76 


.82 


3 


95 


1 


11 


1 


38 


89 


2.81 


1.05 


4 


00 


1 


19 


1 


43 1 


37 


2.86 


.84 


4 


05 


1 


00 


1 


62 


99 


2.90 


.90 


4 


10 


1 


09 


1 


81 


77 


2-95 


.60 


4 


14 


1 


09 


1 


86 1 


62 


3.00 


.76 


4 


19 




98 


1 


90 1 


03 


3-05 


1. 00 


4 


24 


1 


27 


1 


95 


73 


3 09 


■97 











70 



MENTAL FATIGUE DURING CONTINUOUS EXERCISE 



TABLE XXVI (Continued) 



Number 


of Columns 


Number 


of Columns 


Number of Columns 


C. T. 


Average 


C. T. 


Average 


C. T. Average 




ofA.D. 




ofA.D. 


of A 


.D. 






3-14 


1.02 


4.29 1 


38 


2.00 


.48 


3 


19 


• 7i 


4 


38 1 


07 


2.05 


.78 


3 


24 


•97 


4 


43 1 


12 


2.O9 


■92 


3 


29 


1 .04 


4 


48 


90 


2. 14 


.89 


3 


33 


.83 


4 


52 1 


21 


2. 19 


•95 


3 


38 


1 .11 


4 


57 1 


08 


2.24 


.83 


3 


43 


1 .09 


4 


62 1 


15 


2.29 


115 


3 


48 


•89 


4 


67 1 


11 


2-33 


1 .01 


3 


52 


1. 21 


4 


71 1 


49 


4.76 


1. 16 


5 


33 


1 .02 


6 


09 1 


03 


4.81 


1 . 11 


5 


43 


1. 81 


6 


14 1 


39 


4.86 


1.84 


5 


48 


1 .26 


6 


19 


99 


4.9O 


1. 61 


5 


52 


1 .46 


6 


28 1 


08 


4-95 


•97 


5 


57 


i-54 


6 


43 1 


30 


5.00 


.67 


5 


62 


1. 10 


6 


48 1 


22 


505 


1 .24 


5 


7i 


1 .01 


6 


57 


95 


509 


1. 14 


5 


76 


1. 14 


6 


62 1 


14 


5- H 


1. 14 


5 


86 


.86 


6 


76 1 


32 


519 


1. 16 


5 


90 


.87 


6 


90 1 


28 


5-24 


i-34 


5 


95 


.46 


6 


95 1 


17 


529 


.98 


6 


00 


.86 


7 


05 


78 










7 


14 1 


44 










7 


19 1 


38 










7 


48 1 


4i 










7 


57 1 


3i 










7 


67 1 


85 










7 


71 1 


35 










7 


80 1 


35 










8 


00 1 


33 










8 


14 1 


04 










8 


52 


98 










8 


71 1 


59 










9 


33 1 


49 












11 


52 1 


65 



Mi 



VARIABILITY OF THE INDIVIDUAL 



TABLE XXVII 



71 



Showing Data of Foregoing Table Con 


ibined into Twelve Groups 




Average 


C. T. 


ofA.D. 


■ 43 to 1.90 


•85 


1.95 to 2.38 


.88 


2.43 to 2.86 


1 .02 


2.90 to 3.33 


.88 


3.38 to 3.81 


1 .07 


3 . 86 to 4.29 


1 .10 


4.38 to 4.76 


1. 14 


4.81 to 5.24 


115 


5.29to 5.71 


1.28 


5.76 to 6.19 


•95 


6.28 to 6.62 


1. 14 


6 . 76 to 1 1 . 52 


1-34 



The data of Table XXVI could not be easily handled in a graphic representa- 
tion, consequently it was combined into twelve groups as in Table XXIII. In 
this particular table we proceed as nearly by steps of .43 of a column as possible. 
The first and last groups of the series could not be well made to go by the step. 



TABLE XXVIII 

Showing Central Tendencies and Corresponding Average A. D. of 

Columns Attempted by Groups of Individuals of Seventh and 

Eighth Grades. There are 127 Groups 



Number 


of Columns 


Number 


of Columns 


Number 


of Columns 


C. T. 


Average 


C. T. 


Average 


C. T. 


Average 




ofA.D. 




of A.D. 




ofA.D. 


2. 14 


.70 


5- 2 9 


•65 


8.00 


2.22 


2.43 




68 


5 


33 




62 


8 


05 


1 


13 


2.76 




58 


5 


38 




94 


8 


09 




79 


2.81 




61 


5 


43 




79 


8 


14 




4i 


2.90 




61 


5 


48 


1 


04 


8 


24 




67 


2-95 


1 


17 


5 


52 




77 


8 


62 


1 


13 


3.00 




29 


5 


57 




82 


8 


7i 




74 


305 




54 


5 


62 




73 


8 


81 




92 


309 




53 


5 


67 




65 


8 


86 


1 


12 


3-19 


1 


15 


5 


7i 




92 


9 


09 




88 


3 24 




67 


5 


76 


1 


05 


9 


29 




64 


329 




62 


5 


81 




57 


9 


33 


1 


27 


3-33 




5i 


5 


86 




81 


9 


38 




93 


3-38 




69 


5 


90 




79 


9 


52 


1 


02 


3-43 




53 


5 


93 




66 


9 


57 




88 



72 



MENTAL FATIGUE DURING CONTINUOUS EXERCISE 



Number of Columns 



TABLE XXVIII {Continued) 
Number of Columns 



Number of Columns 



c 


7\ Average 


C. T. A 


verage 


C. T. Average 


ofA.D. 


ofA.D. 


ofA.D. 


3-52 


69 


6.00 


72 


9.67 


92 


3 


57 


•79 


6.05 


83 


9.71 


84 


3 


67 


64 


6.09 


64 


10.24 1 


03 


3 


7i 


90 


6. 14 


75 


10.57 


89 


3 


76 1 


20 


6.19 


72 


10.62 


9i 


3 


81 


62 


6.24 1 


H 


10.71 


99 


3 


90 


88 


6.29 


9i 


10.76 


89 


3 


95 1 


14 


6-33 1 


24 


11 . 19 


81 


4 


00 


76 


6.38 


81 


1 1 • 43 1 


29 


4 


05 


76 


6.43 


83 


1 1 . 62 2 


77 


4 


09 


67 


6.52 


83 


11.86 5 


H 


4 


H 


92 


6-57 


69 


13-09 1 


63 


4 


19 


65 


6.62 


95 






4 


24 


65 


6.67 


70 






4 


29 


72 


6.71 


72 






4 


33 


68 


6.76 


65 






4 


38 


72 


6.86 


61 






4 


43 


20 


6.90 


63 






4 


48 


51 


6-95 


7i 






4 


52 1 


10 


7-05 


89 






4 


57 


59 


7.09 


98 






4 


62 


69 


7.14 


30 






4 


67 


74 


7.19 


61 






4 


7i 


57 


7.24 


56 






4 


76 


55 


7.29 


92 






4 


81 


99 


7-33 


96 






4 


86 


68 


7-38 


64 






4 


90 


45 


7-43 


90 






4 


95 


78 


7.48 1 


69 






5 


00 


38 


7-52 


71 






5 


05 


70 


7-57 


68 






5 


09 


68 


7.62 


87 






5 


19 


74 


7.71 


97 






5 


24 1 


26 


7.76 


88 










7.82 


83 












7-95 


88 







The data of Table XXVIII could not be readily handled graphically, and were 
consequently combined into twelve groups as in Table XXV. In this particular 
table we proceed as nearly by steps of .7 of a column as possible, but it is difficult 
to do this because at the beginning and ending of the series — and in the middle 
— the numbers were so very much scattered. The best grouping was made that 
could be made. This does not impair the mathematical value of the graph. 



VARIABILITY OF THE INDIVIDUAL 



73 



TABLE XXIX 

Showing Data of Foregoing Table, Combined into Twelve Groups 



C. T. 



2 . 14 tO 


2.90 


2.95 to 


405 


4 . 09 to 


4.76 


4.81 to 


5-48 


5.48 to 


6.19 


6 . 24 to 


6.90 


6.95 to 


7.62 


7.71 to 


8.24 


8 . 62 to 


8.81 


8.86 to 


9.71 


10.24 to 


10.76 


1 1. 19 to 


13.09 



Average of 
A.D. 

64 
75 
66 
76 

77 
82 
81 
98 
93 
94 
94 
34 



The actual facts for the present test are seen on comparing the 
average variability with the absolute measure of performance. (See 
the accompanying tables — XXII-XXVIII — which give, for the indi- 
viduals having the same central tendency, the average of their 
A. D.'s.) Each of these tables is followed by a regrouping which 
brings out more fully the tendency of the A. D.'s to increase with 
the C. T. 

In the absence of any universally accepted law, we can take these 
figures (Tables XXII, XXIV, XXVI, XXVIII) as our basis and 
see what law of dependence would fit them best. We have assumed 

Var. 
that this law would have the form r T a = C. and find what value 

of the unknown n will give best agreement with this law. That is, 
we are to find such a root of the C. T. as will give the most constant 
quotient when divided into the corresponding variability. 

Thus two methods were used for determining what value of n 
gave the closest approximation to a constant ratio: 

1. Find for what value of n the variability of the quotient is least. 

2. Observe for what value of n the curve approaches most closely to the 
horizontal line. 



74 MENTAL FATIGUE DURING CONTINUOUS EXERCISE 

Tables XXX, XXXI, XXXII, XXXIII give the Average, Aver- 

x 
age Deviation, and Probable Error for each value of — in attempts 

ya 

and accurate performance. 



TABLE XXX 

Showing for Accurates of Third and Fourth Grades the Central Tendency and 

x 
Average Deviation of Different Values of — , where x = A. D., y=C. T. 

yn 



Values 


of 


X 

y 


Values 


of 


X 

yih 


Values 


of 


X 
y\ 


Values 


of 


X 


Values 


of 


X 

y—* 


Values 


of 


X 

y-h 


Values 


of 


X 

y\ 


Values 


of 


X 

y\ 


Values 


of 


X 

y\ 


Values 


of 


X 
y\ 


Values 


of 


X 

yis 


Values 


of 


X 



Average 


.489 


A. D. 


.302 


P. E. 


•254 


Average 


•549 


A. D. 


. 1227 


P. E. 


. 104 


Average 


■559 


A. D. 


.119 


P. E. 


. 100 


Average 


•569 


A. D. 


.1065 


P. E. 


.090 


Average 


■577 


A. D. 


. 1011 


P. E. 


.085 


Average 


•593 


A. D. 


. 10069 


P. E. 


.084 


Average 


.613 


A. D. 


.088 


P. E. 


•075 


Average 


.646 


A. D. 


.090 


P. E. 


.076 


Average 


.691 


A. D. 


.096 


P. E. 


.081 


Average 


.7089 


A. D. 


.108 


P. E. 


.091 


Average 


.7283 


A. D. 


.111 


P. E. 


.094 


Average 


•793 


AD. 


.150 


P. E. 


.127 



VARIABILITY OF THE INDIVIDUAL 75 

TABLE XXXI 

Showing for Attempts of Third and Fourth Grades the Central Tendency 

x 
and Average Deviation of Different Values of — 

Average .241 A. D. .130 P. E. .012 

Average .376 A. D. .126 P. E. .011 

Average .453 A. D. .130 P. E. .011 

Average .501 A. D. .167 P. E. .016 

Average .560 A. D. .192 P. E. .016 

Average .596 A. D. .212 P. E. .019 

Average .615 A. D. .225 P. E. .017 

Average .700 A. D. .290 P. E. .026 

TABLE XXXII 

Showing for Accurates of Seventh and Eighth Grades the Central Tendency 

x 
and Average Deviation of Different Values of — 

Average .329 A. D. .1431 P. E. .011 

Average .558 A. D. .1133 P. E. .009 

Average .684 A. D. .1057 P. E. .008 

Average .766 A. D. .1196 P. E. .091 

Average 1.069 A. D. .2079 P. E. .054 



Values of 


X 

y 


Values of 


X 

y\ 


Values of 


X 

y\ 


Values of 


X 

yi 


Values of 


X 

yi 


Values of 


X 


Values of 


X 

y ia 


Values of 


X 



Values of 


X 

y 


Values of 


X 


Values of 


X 


Values of 


X 

yi 


Values of 


X 



76 MENTAL FATIGUE DURING CONTINUOUS EXERCISE 

TABLE XXXIII 

Showing for Attempts of Seventh and Eighth Grades the Central Tendency 

x 
and Average Deviation of Different Values of — 

-Vn 



Values of 


X 

y 


Values of 


X 

yh 


Values of 


X 
y\ 


Values of 


X 

yi 


Values of 


X 



Average 


.148 


A. D. 


.048 


P. E. 


.004 


Average 


•346 


A. D. 


.085 


P. E. 


.006 


Average 


.467 


A. D. 


.107 


P. E. 


.008 


Average 


•542 


A. D. 


.116 


P. E. 


.009 


Average 


.86 


A. D. 


•304 


P. E. 


.0228 



Explanation 

Tables XXXIV, XXXV, XXXVI, and XXXVII give the different values of 

x 

— combined into twelve groups. (See Figures 13, 14, 15, and 16.) 

X 

Figures 13 to 16 show graphically the position of each value of — on a vertical 

y a 

scale for increasing total performance on a horizontal scale. 



Total 



TABLE XXXIV 

Accuracy, Third and Fourth Grades, Values 



ys 



Average Average Average Average Average Average Average 







y o 


19 


y* 


yrr* 


y—> ym 


1 to 6 


.40 


1.67 


82 


79 


74 


.69 


72 


7 to 12 


.67 


■ 99 


82 


85 


80 


.81 


78 


13 to 18 


.65 


• 59 


62 


62 


62 


• 63 


61 


19 to 24 


•75 


.48 


60 


60 


62 


.63 


64 


25 to 30 


•83 


.42 


59 


59 


61 


.62 


64 


31 to 36 


.87 


36 


55 


56 


59 


.60 


62 


37 to 42 


.88 


• 31 


5i 


52 


55 


• 56 


60 


43 to 48 


.92 


.28 


49 


5i 


53 


• 55 


57 


49 to 54 


.81 


.21 


34 


42 


45 


.46 


49 


55 to 60 


.84 


.20 


40 


4i 


44 


.46 


48 


61 to 73 


.90 


• 19 


40 


4i 


44 


.46 


48 


76 to no 


1 .09 


.16 


41 


43 


47 


• 49 


52 



VARIABILITY OF THE INDIVIDUAL 



77 



Total 



TABLE XXXIV {Continued) 
Average Average Average Average Average 





y* 


yx 


yt 


ys 


y~o 


I to 6 


62 


67 


50 


47 


46 


7 to 12 


76 


74 


71 


70 


69 


13 to 18 


63 


64 


64 


64 


64 


19 to 24 


65 


67 


70 


71 


72 


25 to 30 


66 


70 


74 


75 


78 


31 to 36 


65 


70 


76 


78 


80 


37 to 42 


62 


66 


74 


77 


79 


43 to 48 


62 


69 


75 


79 


81 


49 to 54 


53 


59 


64 


69 


71 


55 to 60 


51 


59 


66 


65 


72 


61 to 73 


54 


61 


69 


74 


77 


76 to no 


59 


69 


79 


86 


90 



TABLE XXXV 

Attempts, Third and Fourth Grades, Values 



Total A 


ver- Aver- Aver- A 


ver- A 


ver- A 


ver- A 


ver- A 


ver 


Number of 


age 


age 


%ge 


age 


age 


age 


age 


age 


Columns 


X 


X 


X 


X 


X 


X 


X 


X 






y 


yh 


y% 


y\ 


y\ 


y\ 


yiz 


4 to 24 


46 


54 


48 


46 


46 


46 


46 


46 


25 to 30 


45 


28 


32 


38 


38 


40 


41 


42 


31 to 36 


58 


36 


43 


46 


49 


49 


49 


53 


37 to 42 


5i 


18 


30 


35 


39 


42 


45 


46 


43 to 48 


59 


18 


33 


36 


4i 


48 


5i 


53 


49 to 54 


63 


17 


32 


41 


45 


49 


54 


55 


55 to 60 


55 


13 


27 


35 


39 


44 


48 


48 


61 to 66 


73 


17 


32 


46 


49 


56 


60 


63 


67 to 74 


69 


H 


3i 


40 


46 


52 


57 


59 


75 to 80 


67 


12 


28 


39 


44 


50 


54 


57 


81 to 97 


81 


13 


32 


44 


51 


60 


62 


57 


98 to 191 2 


4i 


23 


54 1 


11 1 


34 1 


63 1 


78 1 


9i 



78 



MENTAL FATIGUE DURING CONTINUOUS EXERCISE 



TABLE XXXVI 



Accuracy, Seventh and Eighth Grades, Values of 



V" 



Total 


Average Average Average 


Average Avi 


vrag 


Columns 


X 


X 


X 


X 


X 






y 


y\ 


yi 


y~\ 


9-40 


.85 


81 


80 


.82 


*3 


41-50 


.88 


41 


60 




67 


75 


51-60 


1 .02 


39 


63 




74 


80 


61-70 


.88 


21 


52 




60 


64 


71-80 


1 .07 


30 


58 




68 


79 


81-90 


1 . 10 


27 


54 




69 


77 


91-100 


1. 14 


25 


53 




69 


78 


IOI-IIO 


115 


23 


52 




67 


77 


III-I20 


1.28 


23 


55 




73 


86 


I2I-I30 


•95 


17 


35 




52 


61 


I3I-I40 


1. 14 


18 


45 




61 


7i 


I4I-242 


i-34 


17 


48 




67 


80 



TABLE XXXVII 

x 
Attempts, Seventh and Eighth Grades, Values of — 



Total 



Average Average Average Average Average 



Columns 


X 


X 


X 


X 


X 






y 


yi 


yi 


yi 


45-6i 


64 


249 


•397 


464 


502 


62-85 


75 


215 


•403 


495 


542 


86-100 


66 


153 


.296 


405 


458 


101-115 


76 


148 


•335 


429 


507 


111-130 


77 


131 


.316 


424 


524 


I3I-I45 


82 


126 


•329 


441 


515 


146-160 


84 


143 


.301 


415 


495 


162-173 


98 


122 


•346 


488 


581 


181-185 


93 


107 


•315 


452 


507 


186-214 


94 


IOI 


.312 


451 


542 


215-221 


94 


089 


.289 


437 


527 


226-275 2 


34 


196 


.672 1 


on 1 


254 



■■ 



m 



VARIABILITY OF THE INDIVIDUAL 

■Mt/e/npfe 3n) an* 4M Grades - ~ ]/a/aes 



ft ' 




y 

Y 

% 

X V *-■*■ + + 



IS 

h* 

hi 

/.* 

u 

f 

J 

.7 
..(, 

,6' 
.9 
.3 

.V 

] 

./ 



4-34 25-30 31-36 37-4Z 43-48 49-5* 55-60 61-66 6T-T4- , 75"-8o~8/-9y 98-191 

TOTAL.. COLUMNS 

Corrected Variability in Attempts 
Figures 13 and 14 give the graphical representation for the 
attempts data of corrected variability for the younger and older 
groups respectively. 



80 MENTAL FATIGUE DURING CONTINUOUS EXERCISE 

Attempts Ttf.and 8tt.Graetesy*fa/ ues 
tr>£l t I 



.* 
,7 

y 



j 




"X. 









^ •» 






-*T 



■§" 






*— 



H «t 



VARIABILITY OF THE INDIVIDUAL 8l 

For the Third and Fourth grades attempts, Figure 13 shows the 
— 1, — and — r lines to be nearly horizontal, but the preference goes 

y? yi y-i 

X 

to the —j value as it is the most nearly horizontal line of those lines 

y? 



I 



\f //tcurafeS -Jretrfr/i.fcnJcs ji V^/ut 




"7TE 7-/1. 13-1* /f-ifts-J p-JL w Wt* *f-W jp& y-73 -jiftij 
Total Columns 



and besides the —, series has the smallest average deviation of all 

yi ° 

X 

the different series of the — values. 

yn 

As to the attempts data of corrected variability for the Seventh 
and Eighth grades, the - values and the -7 values compete most 

y y? 



82 MENTAL FATIGUE DURING CONTINUOUS EXERCISE 

flccur&Jes- K- 8"'6rc?c/es ft Values 



1-tf 

13 

(•' 

f.o 

■1 
% 
•7 
♦6 

if 

$ 

v 

I 



{ y* 

_x 

X 

yi 

_X 

y 






&£./£ 



***** * 






& 



A 
s^ ,-. r \ 

V-. /\\ / — .,. AW / 

w a> >\ / --•' 



V 



\ V- 



.--*■ 



V 



/ o 9_^ 4 ,-5 5/. eo 6 |_yo 71-80 61-90 9l-ioo /oi-ito 111-120 121-130 Ql-i4-oi«i»24Z 

strongly for the preference. We have chosen here, however, the 
- line, since it appears to be the most nearly horizontal one and the 

y 

judgment seems justified by the fact that the average deviatioh of 



HUB 



VARIABILITY OF THE INDIVIDUAL 



83 



the - series is smaller than that of the other series. But the experi- 

y 

menter thinks that the cause of this inconsistency is due to the 
fact that some of the subjects at the last attempted too recklessly 
and thus impaired the data to a small extent. If this had not hap- 
pened the y* value would have been, the writer believes, the chosen 
value of y k . (Figure 14.) 






n - * " JTc cur* /eS - 

7***1** ■- jrtUtftr - 




F, 



■f'7 



Figure 17 gives the different positions on a vertical scale for the A. D. of each 

x 
— series for both groups in both attempts and accurates. In the case of the 

. . X 

Third and Fourth grades, in attempts, the curve drops lowest for the -7 series; 

■v 2 
x 
but in accurates it is lowest in the — series of values. In the case of the Seventh 

. x 

and Eighth grades, in attempts, the curve is lowest in the - series; but in the 

x 
accurates it goes lowest in —1 as it did in the accurates for the younger children. 
3/3 



84 MENTAL FATIGUE DURING CONTINUOUS EXERCISE 

Corrected Variability in Accurate Performance 
For corrected variability in accurate performance of Third and 
Fourth grades, Figure 15 shows the lines for values of—, — and — 

-y? ys yf 

X 

(when these are taken respectively as in the expression — ) to be 

yn 

all of them nearly horizontal with the preference for a value between 
y* and y* values. We have taken, however, the line representing the 
y 11 value as the one most nearly horizontal of those in the figure. 
Also this value has the smallest average deviation from the average. 
And since these two criteria are those which shall decide in the case, 

Var. 
,~ „,i = C. is the formula taken here. 
(C. T.y 

What has been said of the Third and Fourth grades group may 

also be said of the Seventh and Eighth grades group, Figure 16. 

While the — , — and — lines are all nearly horizontal, the line 

y? yn yi 

representing the y 3 values is probably the one most nearly hori- 
zontal; and since the y* series of values has the smallest average 

x 
deviation, we give the preference to this value of — and so 

Var. . y* 

, _ „ .1 = C. is the formula taken here for this data. However, it 

(c. T.y 

is possible here as above that a value lying somewhere between 

y* and y* is the correct one for the data of accurate performance. 

I think these results agree for the total work and for the accurate 

x 
work. Total work gives greatest constancy at — for Third and 

yi 

Fourth grades and - for Seventh and Eighth grades. Accurate 

y 

work, in the handling of these data gives, or very close to, — in both 

y* 

the younger and older groups. It is likely that the data do not lend 

themselves in their handling to bearing out the theoretical facts. 

x 
Theoretically this should be — . 

yi 



■■»■!■■ 



VARIABILITY OF THE INDIVIDUAL 85 

Variability and Performance 

Var. Var. 

Now, if we accept the formula in one case r T \ = C, or _ _ i = C, 

as fitting the general run of our facts, having based our correction 
upon the general run of our own data, of course we cannot find 
whether those who do less or do more are more variable since what 
we have done shows them equally variable. 

But we can from this graph of the accepted law of dependencies 
see if there are any eccentricities not according to the normal. We 
may say that the group has variability in excess of the general run 
of the data, or that it is close to the general run of the data. 

In all the graphs illustrating the accepted law of dependencies 
we find the last one or two ratios departing, or so tending, from 
the norm and likewise the first one or two. 

In the case of the accurate performances for the younger group, 
this departure from the norm is only slight (see Figure 15 — y" line). 
With the older group the departure at beginning and end is a little 
more pronounced (Figure 16). But in the case of the attempts data 
the departure is quite pronounced, especially at the end of the 

-r and - lines, for both groups. We may then say that this shows 

a tendency for the subjects who attempt most, and also for those 
who attempt least, to exceed the normal variability to some extent. 
This surplus of variability in the slowest and quickest workers is 
probably due to the fact that they show, more than the medium 
workers, a progressive change throughout the course of the work, 
the quickest workers increasing their speed as the work proceeds, 
and the slowest workers gradually slackening (See pp. 49-54). 



-M 



VITA 

THOMAS RUSSELL GARTH 

Born at Paducah, Kentucky, December 24, 1872. 

Entered Union City Public High School, 1891. 

Completed High School course at Warren Academy, Denver, Colorado, and 

diploma granted 1905. Four years of High School work. 
Entered University of Denver, September, 1905. 
Graduated from same June, 1909, with A.B. degree. 
Post-graduate work at University of Denver for one year, 1909-1910. 
Degree of Master of Arts granted in June, 1910. 
Graduate student in Columbia University, 1912-1913, 1915-1916. 



V t~i f 



Deacidified using the Bookkeeper process. 
Neutralizing agent: Magnesium Oxide 
Treatment Date: Nov. 2004 

PreservationTechnologies 

A WORLD LEADER IN PAPER PRESERVATION 

1 1 1 Thomson Park Drive 
Cranberry Township, PA 16066 
(724) 779-21 1 1 



LIBRARY OF CONGRESS 

HI! III! II II 1 1 II III III II II 



013 228 035 6 



